Trigonometry question
Given the following function, choose the graph with the two possible angles with the domain 0[tex]\leq[/tex]0[tex]\leq[/tex]360 degrees.
1. sin0 = -2/3
2. sec0 = 2/1
3. tan0 = 4/5
4. csc0 = -3/2
5. cos0 = -3/5
Answers
The graphs that give the possible solution to the trigonometric functions are as follows
[tex]1. \ sin(\theta) = \dfrac{-2}{3};\ graphs \ 2\ and \ 3[/tex]
[tex]2. \ sec(\theta) = \dfrac{2}{1};\ graph \ 3[/tex]
[tex]3. \ tan(\theta) = \dfrac{4}{5};\ graph \ 3[/tex]
[tex]4. \ csc(\theta) = \dfrac{-3}{2};\ graph \ 2\ and \ 3[/tex]
[tex]5. \ csc(\theta) = \dfrac{-3}{5}\ graph \ 1[/tex]
What is a trigonometric function?A trigonometric function specifies the relation between two side lengths and an interior angle of a right triangle.
1. The given function is sinθ = -2/3
The definition of sin(θ) is [tex]sin(\theta) = \dfrac{Opposite\ side \ length}{Length \ of \ the \ hypotenuse\ side}[/tex]
From the equation, [tex]sin(\theta) = \dfrac{-2}{3}[/tex], which can be taken as the form, [tex]sin(\theta) = \dfrac{-y}{\sqrt{x^2+y^2} }[/tex], therefore, the opposite side leg, y, will be in the third or fourth quadrant, where the y-value is negative.
The possible graphs are therefore, Graph 2, and Graph 3
2. [tex]sec(\theta) = \dfrac{2}{1}[/tex]
Therefore, [tex]cos(\theta) = \dfrac{1}{2}[/tex]
The definition of cos is [tex]cos(\theta) = \dfrac{Adjacent\ side \ length}{Length \ of \ the \ hypotenuse\ side}[/tex]
Therefore, for the angle in standard position, [tex]cos(\theta) = \dfrac{x}{\sqrt{x^2+y^2} }[/tex]
The adjacent side of the angle is in the positive x-axis, which gives an angle in the Quadrant I or Quadrant IV
The only possible option is graph 3
3. [tex]tan(\theta) = \dfrac{4}{5}[/tex]
The definition of the tangent of an angle is: [tex]tan(\theta) = \dfrac{Opposite\ side \ length}{Length\ of\ the \ Adjacent\ side}=\dfrac{y}{x}[/tex]
Which gives a point at (x, y) or (-x, -y), which are points in Quadrant I and Quadrant III respectively.
The possible solution is therefore graph 3
4. [tex]csc(\theta) = \dfrac{-3}{2}[/tex]
Which gives, [tex]sin(\theta) = \dfrac{-2}{3}[/tex]
Given that the y-value is negative, the possible angle is in Quadrant 3 or 4.
The possible solution is, therefore, graph 2 or 3
5. [tex]cos(\theta) = \dfrac{-3}{5}[/tex]
The x-value is negative; therefore, the angle is in either Quadrant II or Quadrant III
The solution is the graph 1
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Related Questions
Help please I will give you an brainelist
Answers
Answer:
Table A
Step-by-step explanation:
Table A because there is a pattern and proportion relation shop has patterns
3^4x=3^6x x 3^5x-14
Answers
Answer:
-0.009
Step-by-step explanation:
put it on desmos
josefina is inscribing a square in a circle with center c. she first uses a straight edge to draw a diameter of the circle through the center. what is her next step?
Answers
The step that is Josefina next step is D. Use a straight edge to connect the four point.
How to illustrate the information?The processes for building a square inscribed in a circle are as follows:
Make a circle with the center c.
Now, using a straightedge, draw the diameter of a circle.
Next, using a compass, draw a perpendicular bisector of the diameter and then, using a straightedge, locate the spots on the circle where the perpendicular bisector meets.
Then, using a straightedge, join the four points to form the needed square.
In conclusion, the correct option is D.
The complete question is written below.
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Complete question
Josefina is inscribing a square in a circle with center c. She first uses a straight edge to draw a diameter of the circle through the center. Then, using a compass and straight edge, she constructs the perpendicular bisector of the diameter forming another diameter. Which of these steps is her next step?
A. Open the compass to a width equal to the diameter of the circle.
B. Use a straight edge to extend the diameters outside the circle.
C. Open the compass to the distance between consecutive points on the circumference of the circle.
D. Use a straight edge to connect the four point
A mountain road is 5 miles long and gains elevation at a constant rate. After 2 miles, the elevation is 5500 feet above sea level. After 4 miles, the elevation is 6200 feet.(story)
1.Find the elevation of the road at the point where the road begins. (From the story)
2. Describe where you would see a point in part (a) on a graph where y represents the elevation in feet and x represents the distance along the road in miles. (from the story)
Please help and show your work Please.
Answers
Using a linear function, it is found that:
1. The elevation where the road begins is of 4800 feet.
2. The initial elevation is the intercept of the graph, that is, the value of y when the function crosses the y-axis.
What is a linear function?A linear function, in slope-intercept format, is given according to the following rule:
y = mx + b
In which the coefficients are described as follows:
The coefficient m is the slope of the function, which is the rate of change of the function, given by the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).In the context of this problem, we are given two points:
(2, 5500) and (4, 6200).
The slope of the function is given by the change in y of these points divided by the change in x of these points, hence:
m = (6200 - 5500)/(4 - 2) = 350.
Hence:
y = 350x + b.
For both items, we need to find the intercept of the function, that is, the numeric value of y when the function crosses the y-axis(Item 2).
We have that when x = 2, y = 5500, hence the initial elevation of the road can be found as follows:
5500 = 350(2) + b
b = 5500 - 350(2)
b = 4800 feet.
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Solve the rational equation for x and state all x values that are excluded from the solution set. If there is more than one excluded value then separate them with a comma and do not include any spaces. If a value is not an integer then type it as a decimal rounded to the nearest hundredth. \frac{5}{x+1}+\frac{1}{x-3}=\frac{-6}{x^2-2x-3} Solving for x gives us x=AnswerThe value for x cannot equal Answer
Answers
Answer:
Solving for x gives us x = 1.33
The value for x cannot equal 3,-1
Explanation:
The initial expression is:
[tex]\frac{5}{x+1}+\frac{1}{x-3}=\frac{-6}{x^2-2x-3}[/tex]The denominator of the right side can be factorized as (x - 3)(x + 1) because -3 and 1 multiply to -3 and sum to -2. So, we can rewrite the expression as:
[tex]\frac{5}{x+1}+\frac{1}{x-3}=\frac{-6}{(x-3)(x+1)}[/tex]Now, we can sum the expression on the left side to get:
[tex]\frac{5(x-3)+(x+1)}{(x-3)(x+1)_{}}=\frac{-6}{(x-3)(x+1)}[/tex]Both sides have a denominator of (x-3)(x+1), so we need to exclude the values where this denominator is equal to 0. Those values are:
x - 3 = 0
x - 3 + 3 = 0 + 3
x = 3
x + 1 = 0
x + 1 - 1 = 0 - 1
x = -1
So, the values of x cannot be equal to 3 and -1.
Then, if the denominators are the same, we can find the solution of the equation, making equal the numerators, so we need to solve:
[tex]5(x-3)+(x+1)=-6[/tex]Solving for x, we get:
[tex]\begin{gathered} 5(x_{})+5(-3)+x+1=-6 \\ 5x-15+x+1=-6 \\ 6x-14=-6 \\ 6x-14+14=-6+14 \\ 6x=8 \\ \frac{6x}{6}=\frac{8}{6} \\ x=1.33 \end{gathered}[/tex]Therefore, the answers are:
Solving for x gives us x = 1.33
The value for x cannot equal 3,-1
2, 8, 14, 20, 26... Look at the pattern above. What will the next number in the pattern be?
Answers
Answer:
32
Step-by-step explanation:
you just keep adding 6, simple :)
Answer:
32
Step-by-step explanation:
pattern: +6
∴ next number in pattern = 26 + 6
= 32
The diagram represents two statements: p and q.
P
A
B
9
C
Which represents regions A, B, and C?
O p V q
Op-q
O q^p
Q q-p
Answers
Option A, p V q is the correct answer. We can also say it as p union q.
What do you mean by union in mathematics?
The set containing all the elements in a collection of sets is referred to as the union (denoted by ) in set theory. It is one of the fundamental operations that allows sets to be joined together and connected to one another. A union of zero (0) sets is referred to as a nullary union, because it is by definition equivalent to the empty set.
The diagram shown below represents two statements which are p and q.
Here in the diagram,
A covers the region in which only p is true.
B covers the region in which both p and q are true.
C covers the region in which only q is true.
The combine region of A, B, and C covers the region in which either p is true or q is true.
Therefore the region of A, B, and C is the union of p and q. It can be written as p v q or p ∪ q.
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If m∠LMN=43°
and ∠LMN≅∠OMP,
what is m∠NMP?
Answers
The measure of angle ∠NMP will be equal to 94 degrees.
What is congruency of triangles?Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. We can prove two triangles to be congruent using any of the four mentioned rules or criteria's
SSS ruleSAS rule ASA ruleAAS ruleGiven is ∠LMN = 43° and ∠LMN ≅ ∠OMP
Now, since it is given that ∠LMN ≅ ∠OMP, we can say that -
∠LMN = ∠OMP = 43°
Now, assume that ∠NMP equals to β°.
Since, LMO is a straight line, we can write -
∠LMN + ∠NMP + ∠OMP = 180°
43 + β + 43 = 180
β = 180 - 86
β = 94°
∠NMP = β = 94°
Therefore, the measure of angle ∠NMP will be equal to 94 degrees.
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[Refer to the image attached for complete question]
How does the graph of the function f(x) = x³ + 1
compare to the parent function f(x) = x³?
A. shifted up 1 unit
B.
shifted down 1 unit
C. shifted left 1 unit
D. shifted right 1 unit
Answers
When function f(x) = x^3 + 1 compared to its parent f(x) = x^3, it shifted left by 1 unit.
According to the question, given that
function f(x) = x³ + 1 , compare to the parent function f(x) = x³
when function f(x) = x³ + 1 comparing to the parent function f(x) = x³
then shifted left 1 unit.
graph of the function given below
In mathematics, some graphs are frequently seen. As a result, these initial, widespread functions—which also comprise graphs of quadratic functions, square roots, absolute values, cubic, and cube roots—are referred to as parent graphs.
quadratic function graphing
The utmost power or square to which an unknown number or variable can be raised is known as a quadratic function. The parent graph of all other quadratic functions is the function y=x2 or f(x) = x2, which is a quadratic function.
A parabola is the name for any quadratic function's graph. The fundamental shape of a parabola is uniform.
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Eight taken away from a number squared
Translating verbal expressions
Answers
Translating verbal expressions into algebraic expression is 8 - x²
What is algebraic expression?An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.). Terms combine to form expressions. A number, a variable, or a mix of both plus certain operation symbols make up an expression. An equal sign separates two expressions that make up an equation. the sum of 8 and 3, for instance. Example sentence: The result of adding 8 and 3 is 11.
Given Data
Eight taken away from a number squared
Translating verbal expressions into algebraic expression:
Let number squared be x
8 - x²
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During the winter, if the low temperature outside is xx °C, the daily cost to heat a building can be determined using the function f(x)=9\left(1.2\right)^{-x}.f(x)=9(1.2) −x . Find and interpret the given function values and determine an appropriate domain for the function.
Answers
The values of the function are 9 and 1.2 and the domain is -oo <x < oo
How to interpret the function valuesThe equation of the function is given as
f(x) = 9(1.2)⁻ˣ
The above function is an exponential function.
An exponential function is represented as
f(x) = abˣ
Where
a represents the initial value, b represents the rate of growth or decayWhile x and f(x) are the input and output valuesBy comparison, we have
a = 9 and b = 1.2
This means that the function values are 9 and 1.2
The domainRecall that the function is an exponential function.
The domain of an exponential function is the set of all real values
Hence, the domain of f(x) is the set of all real values
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find the value s of x and y
Answers
Answer:
x = 180-35 = 145
y = 35
Hope it helps
Which point is a solution to this system of inequalities?
y < 1/2x - 3y + 2x > 6
A. (7-8)
B. (2-3)
C. (5,-2)
D. (4,1)
Answers
Option C is correct. The (5,-2) point solves the given system of inequalities y < 1/2x - 3 and y + 2x > 6.
What exactly is an inequality?An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.The given system of inequalities is as follows:
y < 1/2x - 3, y + 2x > 6
Substituting (7,-8) in these inequalities,
y < 1/2x - 3
y < 0.5
-8 < 0.5 is true
y + 2x > 6
-8 + 14 > 6
6 > 6 is false
So this is incorrect option.
Similarly, substituting (2,-3) in these inequalities,
y < 1/2x - 3
y < -3
-3 < -2 is true
y + 2x > 6
1 > 6 is false
So this is incorrect option.
Substituting (5,-2) in these inequalities,
y < 1/2x - 3
-2 < -0.5 is true
y + 2x > 6
8 > 6 is true
So, this is correct option.
Therefore, (5,-2) point is a solution to the given system of inequalities y < 1/2x - 3 and y + 2x > 6. So, Option C is correct.
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A coffee distributor needs to mix a(n) Organic Free Trade coffee blend that normally sells for $9.10 per pound with a House coffee blend that normally sells for $12.10 per pound to create 30 pounds of a coffee that can sell for $10.10 per pound. How many pounds of each kind of coffee should they mix?
Answers
Taking into account the definition of a system of linear equations, the coffee distributor needs to mix 10 pounds of House coffee blend and 20 pounds of Organic Free Trade coffee blend.
System of linear equationsA system of linear equations is just a set of two or more linear equations with the same unknowns, of which a common solution needs to be found. That is, the solution is a point (x,y) that satisfies both equations.
In other words, a system of equations is a set of related equations by means of the same variables in which the values of said unknowns must be sought, with which, when replaced, they must give the solution proposed in both equations.
Amount of pounds of each kind of coffeeIn this case, a system of linear equations must be proposed taking into account that:
"o" is the amount of pounds of Organic Free Trade coffee blend that a coffee distributor needs to mix."h" is the amount of pounds of House coffee blend that a coffee distributor needs to mix.You know:
A coffee distributor needs to mix a(n) Organic Free Trade coffee blend that normally sells for $9.10 per pound with a House coffee blend that normally sells for $12.10 per pound.The coffee distributor create 30 pounds of a coffee that can sell for $10.10 per pound.The system of equations to be solved is
o + h= 30
o9.10 + h12.10= 10.10×30
There are several methods to solve a system of equations, it is decided to solve it using the substitution method. This method consists of, having a system that has two equations with two unknowns, isolating one of the unknowns of one of the equations and substituting the expression obtained in the other. You can choose any of the variables and any of the equations. In this way, the value of one of the variables is obtained, which when replaced in the expression obtained in the first step, the other variable is obtained.
In this case, isolating the variable "o" from the first equation:
o=30 -h
Replacing this expression in the second equation:
(30 - h)×9.10 + h12.10= 10.10×30
Solving:
30×9.10 - h9.10 + h12.10= 10.10×30
273 - h9.10 + h12.10= 303
- h9.10 + h12.10= 303 - 273
3h= 30
h= 30÷ 3
h= 10
Remembering that o=30-h, you get:
o= 30 -10
o= 20
This means that they should mix 10 pounds of House coffee blend and 20 pounds of Organic Free Trade coffee blend.
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order from least to greatest. thank you!!
Answers
Answer:
Step-by-step explanation:
1/25 and then .2 and then 1/4
A 5 foot tall person standing near a tree casts a shadow 8 feet long. At the same time, the tree casts a shadow that is 24 feet long. The triangles shown in the diagram are similar.
What is the value of x, the height of the tree?
30 ft.
12 ft.
15 ft.
2.5 ft.
Answers
Answer:
Step-by-step explanation: 12 ft just had a test on this
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llllllllllllllllllllllllllllllllllljvdvw
Answers
13. Write a quadratic equation that will have a solution of only x = 0. Note: this means there will be a double solution of x = 0.
Answers
we have that
A quadratic equation that will have a solution of only x = 0 is given by the equation
[tex]y=x^2[/tex]what is 3 1/5- 1 1/3
Answers
Answer: 1.86667
Step-by-step explanation: i just looked it so it might be wrong
Alyssa has saved up throughout the year and currently has $144.Of that she spent 5/8 at her favorite store.How much money did Alyssa spend at her favorite store?
Answers
Alyssa spent $90 at her favorite shop.
It has to do with algebra.
Describe algebra.the area of mathematics where numbers and quantities are represented in formulas and equations by letters and other generic symbols. There are several sub-branches of algebra, including commutative algebra, abstract algebra, linear algebra, and elementary algebra.
Alyssa currently possesses $144.
She spent 5/8 of that amount at her favorite store.
= (5 * 144) ÷ 8
After solving, we obtain the value $90.
As a result, Alyssa spent $90 at her favorite retailer.
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Petra has 15 yards of fabric to make costumes for a play. If each costume requires 1 1/3 yards how many costumes can she make?
Answers
A fraction is a part of a whole. If Petra has 15 yards of fabric to make costumes for a play. If each costume requires 1 1/3 yards then she can make costumes.
What is Fraction?A fraction is a part of a whole.
Given that Petra has 15 yards of fabric to make costumes for a play.
To make a costume it requires 1 1/3 yards.
We have to find how many costumes she can make from 15 yards.
In this question 15 yards is whole and 1 1/3 is the part of it.
Convert 1 1/3 to a improper fraction
1 1/3 =4/3.
Now divide 15 by 4/3.
15/4/3
=15/1×3/4
Forty five divided by four.
=45/4
We get eleven point two five.
=11.25
Hence 11 costumes can she make from yards of fabric.
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choose all the values of b to make the the following statement true:7/30 =28/b
Answers
To find the values of b that make the statement true you solve the equation for b:
Multiply both sides of the equation by b:
[tex]\begin{gathered} b\cdot\frac{7}{30}=b\cdot\frac{28}{b} \\ \\ b\cdot\frac{7}{30}=28 \end{gathered}[/tex]Multiply both sides of the equation by 30/7
[tex]\begin{gathered} b\cdot\frac{7}{30}\cdot\frac{30}{7}=28\cdot\frac{30}{7} \\ \\ b=\frac{28\cdot30}{7} \\ \\ b=\frac{840}{7} \\ \\ b=120 \end{gathered}[/tex]Then, the values that make the statement true are: 840/7 and 120c. Write an equation to represent the number of Calories in any number
of grams of trail mix.
Answers
The equation to represent the number of Calories in any number
of grams of trail mix is C = 3x where, c = no. of calories and x = no. of grams of trail mix.
What is calorie?
The term "calorie" with the symbol "cal" generally refer to the big unit in nutrition and food science. It is typical practice to describe the energy content of foods in terms of serving size or weight, the recommended daily calorie intake, metabolic rates, etc. on package labels and in publications. To prevent misunderstanding, some authors advise using the capital C-spelled terms Calorie and Cal instead of other terms. This standard, however, is frequently disregarded.
We can see in the table that 50 grams pf trail mix contain 150 calories.
So, calories in 1 gram = total calories/total grams
calories in 1 gram = 150/50
calories in 1 gram = 3
Now lets take x as a number of grams taken:
So, Total calories in x grams of trail mix = 3x
So, the required equation is:
C = 3x
Where, C = no. of calories in x grams of trail mix.
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find the value of x and a equals -2
Answers
Answer:
If the question was find the value of a when a equal -2, then the answer is a = -2
Larry has $3.10 consisting of quarters, dimes, and nickels. He has twice as many quarters as
dimes and 3 more dimes than nickels. Find the number of each kind of coin.
Answers
Answer:
Larry has 10 Quarters, 5 Dimes and 2 Nickels.
Step-by-step explanation:
Since Larry has 5 Dimes, that's already 50 cents, with twice as many Quarters as Dimes, that gets him to a total of $3.00. But because he has 3 more Dimes than Nickels, he has 2 Nickels, leading to the correct answer of $3.10
(3.4 x 10²) (4 x 10³)
Answers
Answer:
1360000x2
Step-by-step explanation:
Answer: 1,360,000
Step-by-step explanation: First solve the power of's. 10^2 is 100. 10^3 is 1000. Now do 3.4 x 100 which is 340. Then do 4 x 1000 which is 4000.
Now it is (340)(4000) When the parentheses are next to each other you need to multiply. When you do you get 1,360,000
A gallon of paint will cover about 300 square feet of wall space. a painting contractor needs to paint about 32,500 square feet of wall. how many gallons of paint are needed?
Answers
Gallons of paint are needed to paint about 32,500 square feet of wall is 109 gallons.
given:
A gallon of paint will cover about 300 square feet of wall space,a painting contractor needs to paint about 32,500 square feet of wall.
now we can divide our paint area by 300 feet squared per gallon
gallons of paint needed = 32500 /300
= 108.33
since 0.33 is not sold at stores,we need 109 gallons of paint.
Hence Gallons of paint are needed to paint about 32,500 square feet of wall is 109 gallons.
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-7/8u = -21 solve for u and simplify your answer as much as possible
Answers
Answer: u = 1/24
Step-by-step explanation:
-7/8u = -21
Multiply both sides by 8u
(8u) -7/8u = -21 (8u)
-7 = -21 (8u)
Divide by -21
-7/-21 = 8u
1/3 = 8u
Divide by 8
(1/3)/8 = u
When dividing fractions, flip and multiply
(1/3) (1/8) = u
u = 1/24
It works if you plug it back in, hope this helps
-9y+2(5y-2)
Preciso da resposta o Mais rápido possível
Answers
Answer:
y-4
Step-by-step explanation:
Using FUNCTION NOTATION, assume you are given the function: y = 3x - 2. This can be rewritten as
= 3x - 2, since y can be replaced with
Answers
The function notation will be:
f(x) = 3x - 2
Since y (the output) can be replaced with f(x).
How to use function notation?First, we know that a relationship between two variables x and y maps the first variable (called the input) into the second variable (called the output)
In this case, the relationship between x and y is linear, and is of the form:
y = 3x - 2
Particularly, if for each value of "x" that we use we get only one value of y as the output, then the relationship is called a function, and in that case we can write:
y = f(x).
So here to use function notation we just write:
f(x) = 3x - 2
And in that way we know that we have a function.
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