The angles, 60°, [tex]\displaystyle \frac{\pi}{4}[/tex] and [tex]\displaystyle \frac{\pi}{6}[/tex] are special angles that have known trigonometric ratio values.
First part;
The sine and cosine gives the coordinates of the tip of the radius of a unit circle as it rotates P(cos(θ), sin(θ))Second part;
With the knowledge of the sine and cosine of 60°, we have; sin(60°) = sin(120°), sin(240°) = -sin(60°), sin(300°) = -sin(60°)cos(120°) = -cos(60°), cos(240°) = -cos(60°), cos(300°) = cos(60°)Third part;
[tex]\displaystyle \frac{\pi}{4}[/tex] can be used to find the sine and cosine of [tex]\displaystyle \frac{3 \cdot \pi}{4}[/tex], [tex]\displaystyle \frac{5 \cdot \pi}{4}[/tex], and [tex]\displaystyle \frac{7 \cdot \pi}{4}[/tex] [tex]\displaystyle \frac{\pi}{6}[/tex], can be used to find the sine and cosine of [tex]\displaystyle \frac{5 \cdot \pi}{6}[/tex], [tex]\displaystyle \frac{7 \cdot \pi}{6}[/tex], and [tex]\displaystyle \frac{11 \cdot \pi}{6}[/tex]Reasons:
First Part;
Considering a unit circle with the center at the origin of the graph, we have;
The sine of the angle, θ, rotated by the radius is the vertical distance of a point P on the circle which is the location of the radius, from the horizontal axis.
The cosine of the angle, θ, is the horizontal distance of P from the vertical axis, such that we have;
The coordinates of point P = (cos(θ), sin(θ))
In the four quadrant, we have;
First Quadrant; All trigonometric ratios are positive
Second Quadrant; sine is positive
Third Quadrant; Tan is positive
Fourth Quadrant; Cosine is positive
Second part;
We have; At 120°, the point P is the same elevation from the horizontal axis, therefore;
sin(60°) = sin(120°) = 0.5·√3
However, the x-coordinate of the point P is in the negative direction, therefore, we get;
cos(120°) = -cos(60°) = -0.5
Similarly from the quadrant relationship, we have;
240° is in the third quadrant, and it is 60° below the negative horizontal line, therefore;
sin(240°) = -sin(60°) = -0.5·√3
cos(240°) = -cos(60°) = -0.5
300° is in the fourth quadrant, and it is 60° below the positive x-axis, therefore;
sin(300°) is negative and cos(300°) is positive
Which gives;
sin(300°) = -sin(60°) = -0.5·√3
cos(300°) = cos(60°) = 0.5
Third part;
[tex]\displaystyle \frac{\pi}{4} =45^{\circ}[/tex]
[tex]\displaystyle \frac{\pi}{6} =30^{\circ}[/tex]
The sine and cosine of 45° can be used to find the sine and cosine of (180° + 45°) = 225°, (360° - 45°) = 315°
Also, due to the mid location of the angle 45° on the quadrant, we have;
Another angles is the sines and cosine of (90° + 45°) = 135°
Therefore, [tex]\displaystyle \frac{\pi}{4}[/tex], can be used to find the sine and cosine of 135°, 225°, and 315°
[tex]\displaystyle 135^{\circ} = \mathbf{\frac{3 \cdot \pi}{4}}[/tex], [tex]\displaystyle 225^{\circ} = \frac{5 \cdot \pi}{4}[/tex], [tex]\displaystyle 315^{\circ} = \frac{7 \cdot \pi}{4}[/tex]
Therefore,
[tex]\displaystyle \frac{\pi}{4}[/tex] can be used to find the sine and cosine of [tex]\displaystyle \mathbf{\frac{3 \cdot \pi}{4}}[/tex], [tex]\displaystyle \mathbf{\frac{5 \cdot \pi}{4}}[/tex], and [tex]\displaystyle \mathbf{ \frac{7 \cdot \pi}{4}}[/tex]
Similarly, the sine and cosine of, [tex]\displaystyle \frac{\pi}{6}[/tex] = 30° can be used to find the sine and cosine of 150°, 210°, and 330°.
[tex]\displaystyle 150^{\circ} = \frac{5 \cdot \pi}{6}[/tex], [tex]\displaystyle 210^{\circ} = \frac{7 \cdot \pi}{6}[/tex], and [tex]\displaystyle 330^{\circ} = \frac{11 \cdot \pi}{6}[/tex]
[tex]\displaystyle \frac{\pi}{6}[/tex], can be used to find the sine and cosine of [tex]\displaystyle \mathbf{ \frac{5 \cdot \pi}{6}}[/tex], [tex]\displaystyle \mathbf{ \frac{7 \cdot \pi}{6}}[/tex], and [tex]\displaystyle \mathbf{\frac{11 \cdot \pi}{6}}[/tex]
Learn more about the sine and cosine of angles here:
https://brainly.com/question/4372174
Answer:
Step-by-step explanation:
The cosine value of an angle is the x coordinate of the point the angle corresponds to on the unit circle, and the sine value of an angle is the y coordinate of that point. 120, 240, and 300 all form 60 degree reference angles which in turn forms 30-60-90 triangles which help to find the sine and cosine of these corresponding angles. Pi/4 radians converts to 45 degrees which forms a 45-45-90 special triangle on the unit circle which has its own known trigonometric ratio. Pi/6 radians converts to 30 degrees which forms a 30-60-90 triangle on the unit circle which also has a known trigonometric ratio. These ratios help find the sine and cosine of the angles on the unit circle which corresponds to a point on the coordinate plane.
which problem can be solved with the equation 1.75 +(-1.75)=0
x+y=0
Step-by-step explanation:
x= 1.75
y= -1.75
You go to your locker to get some supplies. You grab 3 pens and 6 markers, then you find 2 more markers on the bottom of your locker. Choose the equivalent expressions to represent the number of pens and markers you now have.
BoldItalicUnderline
Billy has 201 packages of postcards. Each package has 18 cards. Use rounding to estimate. About
how many cards does Billy have?
If y varies directly as x, and y = 12 when x = 72, then what is the value of x when y = 3 ?
18
2
1 half
1
6
Answer:
x = 18
Step-by-step explanation:
difference between y = 12, x=72 is 6
so if y = 3 then multiply 3×6 = 18
Answer:
18
Step-by-step explanation:
-33 less than or equal to -4x + 3
Step-by-step explanation:
-33 ≤ -4x + 3
Group like terms
4x ≤ 3 + 33
4x ≤ 36
Divide both sides by 4
4/4x ≤ 36/4
x ≤ 9
Final answer: x ≤ 9
Hope this helps.
Find the equation of the line passing through the point (-1,0) and parallel to the line
y=-1/2x+3/7
A) y= 2x + 2
B) y = -1/2-1/2
C) y = 1/2x+1/2
D) y = - 1/2x+1/2
Answer:
B) y= -½x -½
Step-by-step explanation:
Slope-intercept form
y= mx +c, where m is the slope and c is the y-intercept.
[tex]y = - \frac{1}{2} x + \frac{3}{7} [/tex]
Slope of given line= -½
Since parallel lines have the same slope, slope of unknown line= -½.
y= -½x +c
To find the value of c, substitute a pair of coordinates into the equation.
When x= -1, y= 0,
[tex]0 = - \frac{1}{2} ( - 1) + c[/tex]
[tex]0 = \frac{1}{2} + c[/tex]
[tex]c = - \frac{1}{2} [/tex]
Thus, the equation of the line is y= -½x -½.
Matilda earns 48$ in 4 hours, How many hours does it take her to earn 288$?
Answer:
24
Step-by-step explanation:
If Matilda earns $48 in 4 hours, then she must earn 48/4 (12) dollars per hour. We know she earns $12 per hour, and that she made $288, so we divide the total amount earned (288) by her hourly wage ($12) to find she worked 288/12 or 24 hours.
Matilda will earn $288 in 24 hours.
What are word problems?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
Given is that Matilda earns $48 in 4 hours.
Let us assume that it will take her {x} hours to earn $288.
Then, we can write -
there is earning of $48 in 4 hours.
so, there will be earning of $1 ins (4/48) or (1/12) hours.
hence, she will earn $288 in (1/12 x 288) or 24 hours.
Therefore, Matilda will earn $288 in 24 hours.
To solve more questions on equation modelling, visit the link below -
brainly.com/question/29299318
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What is the slope of the line through (-10, 1) and (0, -4)?
Answer:
-1 / 2.
Step-by-step explanation:
The Slope of a line when given two points:
First establish the two points as (X1, Y1) and (X2,Y2)
you can decide which point is (X1, Y1) and which point is (X2,Y2) in any order
So I choose (X1, Y1) = (-10,1) and (X2,Y2) = (0,-4)
Next use this equation to find the difference in rise/run (rise over run): (Y2 - Y1) / (X2 - X1)
Now we're ready to solve by plugging in our points: ( (-4) - 1 ) / ( 0 - (-10) ) **DON'T FORGET negatives attached to numbers when plugging in**
Solve: (-5) / 10 = -5 / 10 or -1 / 2 reduced by taking out a 5 from top and bottom. So your slope is equal to -1 / 2.
Answer:
-1/2
Step-by-step explanation:
What is the equation on the graph?
Please help!!!
Answer:
y = -1/4x + 2
Step-by-step explanation:
using the slope-intercept form (y=mx+b) m is the slope of the line which is -1/4 because it is decreasing and b is the y-intercept of the line which is 2
What is the range of the relation?
Question 9 options:
{–4, –2,–1, 2}
{–4, 4}
{–3, –2, 0, 2}
{–4, –2, –1, 0, –2}
Answer:
{- 3, - 2, 0, 2 }
Step-by-step explanation:
The range is the y- coordinates of the points
(- 4, - 3 ) , (- 1, - 2 ) , (- 2, 0 ) , (0, 2 )
The y- coordinates are - 3, - 2, 0, 2
Then the range is { - 3, - 2, 0, 2 }
Shanice won 88 pieces of gum playing the bean bag toss at the county fair. At school she gave four to every student in her math class. She only has 8 remaining. How many students are in her class?
Equation:
Answer:
Steps to solve:
Answer:
20
Step-by-step explanation:
88 divided by 4 = 22, She gave 4 gums to each student, 8 divided by 4 = 2.
22 - 2 = 20
HELP ME PLEASEEEEEEEEEEEEEEEEEEEEEEEEE!!!
Answer:
Step-by-step explanation:
from the given information, I would say they are all false since congruent means they are identical in form, whereas these are similar parrellelograms since potentially if you upscaled one it would be close to the other
Convert the following from factored form to standard form.
f\left(x\right)=\left(x+5\right)\left(x-1\right)f(x)=(x+5)(x−1)
Answer:
the mmic is back still swords rund eep
Step-by-step explanation:
Please help everyone!!!!! I will give you brainliest if you answer my question correctly! The average weight of 6 packages is (9m+8) pounds 2 more packages with weights of (12m + 12) pounds and (14m + 12) pounds, are added to the original 6 packages. Find the average weight of the 8 packages.
Answer: 22m + 20
First average the 2 package weights:
(12m+12) + (14m + 12) / 2
(26m + 24) / 2
13m + 12
So the average weight of 2 package is 13m + 12
Now you already know the average of 6 packages that is 9m + 8. So add the 2 package and 6 package average weights.
13m + 12 + 9m + 8
22m + 20
I am not sure unless you or someone else thinks it correct. But thats it, pls forgive me if i am wrong... :(
H.C.F of 378 and 567 and 252
Answer:
Their highest common factor is the number 9
5) So far you have a MP3 Player with 0.5 GB of music already stored on the MP3 player and know that each song is about 0.002 GB of memory. What are the possible numbers of additional songs that you can put on the MP3 player if it holds at most 2 GB?
Answer: Any whole number between 0 and 750, including both endpoints.
One example could be 700 additional songs.
==================================================
Explanation:
x = number of additional songs, some nonnegative whole number
1 song takes up 0.002 GB, so x of them take up 0.002x GB of memory.
Add on the 0.5 GB already used to get the expression 0.002x+0.5 to represent the total amount of storage taken up. We want this expression to be 2 or smaller.
[tex]0.002x + 0.5 \le 2\\\\0.002x \le 2-0.5\\\\0.002x \le 1.5\\\\x \le 1.5/0.002\\\\x \le 750\\\\[/tex]
This says the most songs we can add are 750.
Because x is the number of songs, it doesn't make sense to have x be negative. This means [tex]x \ge 0[/tex] or [tex]0 \le x[/tex] is the case as well.
Combining [tex]0 \le x[/tex] and [tex]x \le 750[/tex] produces the compound inequality [tex]0 \le x \le 750[/tex]
The number of additional songs is any whole number between 0 and 750, including both endpoints.
The roster notation of this set could look like this: {0, 1, 2, ..., 748,749,750}
The triple dots indicate "keep this pattern going". That way we don't have to fill in all 751 values which would be a tedious process.
So you can add on something like 700 songs because it's between those endpoints mentioned, but cannot add something like 800 songs.
Answer:
0 - 750 additional songs
Step-by-step explanation:
current: 0.5 mb
remaining: 2-0.5=1.5 mb
each song: 0.002 gb
take remainig amount of space: 1.5 mb and divide by how much space each song takes: 0.002 mb to find out how many songs can fit in 1.5 mb of space
work:
(total amount of storage-used amount of storage)/storage per song
(2.0-0.5)/0.002
= 1.5/0.002
= 750 songs
what are the possible number of additional songs?
anything up until 750.
4/5=x/100 solve please
Answer:
x = 80
Step-by-step explanation:
4/5 = x/100
100 · 4/5 = 100 · x/100
100 · 4/5= x
80 = x
x = 80
Hence, The Answer is 80.
PLEASE HURRY 40 POINTS
Answer:
3√5
Step-by-step explanation:
Hope this helps you ......
How do you solve this??? I need it fast please help with steps.
(x+3)(x+1)^2(x−4)>0
Answer:
x < -3 or x > 4
Step-by-step explanation:
The product of the factors is 4th-degree, and the leading coefficient is 1 (positive).
The factors tell you the following about the zeros:
x = -3 . . . sign change from + to -
x = -1 . . . graph touches, but no sign change. - on either side of x=-1
x = 4 . . . sign change from - to +
__
The function will be positive for x < -3 and for x > +4.
_____
Additional comments
The value of the function is zero when any of its factors is zero. The value of a factor changes sign when the value of x changes from one side of the 0 to the other. For example, here, we have x+1 as a factor, so x=-1 is a zero. When x = -0.9, the factor is positive (-0.9 +1 = 0.1). When x = -1.1, the factor is negative (-1.1 +1 = -0.1). If this factor were to the first power, it would cause the value of the function to change sign at x=-1.
However, the factor (x+1) has an even power: (x+1)^2. That means when the factor is negative, its square is positive, and when the factor is positive, its square is positive. In short, the factor (x+1)^2 causes the function to be zero at x=-1, but does not make the function change sign there.
The product of all of these factors will result in a polynomial with x^4 as the highest-degree term. That means the function is of even degree. The leading coefficient is 1, so is positive, and the function will generally have a U-shape. The left-most (odd-degree) zero will be where the function changes sign from positive to negative. The right-most (odd-degree) zero will be where the function changes sign from negative to positive. Those zeros are x=-3 and x=+4, respectively. There are no places between these where the function changes sign, so these zeros are the ends of the regions where the function is positive (>0).
i will give you brainiest if correct
Which situation can be represented by the inequality?
x<90
A. There are 90 children at summer camp.
B. Betty is over the age of 90.
C. A kiddie pool holds under 90 liters of water.
D. A refrigerator weighs more than 90 kilograms.
Answer:
c
Step-by-step explanation:
jim writes 10/4words evry day how many words does he write in 10/3 days
Answer:
10/4 per day (2.5 words simplified)
10/3 days he wrote so far (around 3 days simplified)
so in order to find out how much he wrote in total multiply the two numbers together
2.5 x 3 = around 7.5 or 8 words
A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If
Erica has at most $10 to spend on
the cab ride, how far could she travel?
Answer: 12.69 miles or less
Step-by-step explanation:
$10 - $1.75 = $8.25
$8.25/$0.65 = 12.69
PLS HELP ME ASAP
NO LINKS
Answer:a
Step-by-step explanation:
Which of the following is equivalent to 2/9
A. 0.029
B.0.2
C.0.29
D.0.3
E.0.39
Answer:
B would be the answer:))
Step-by-step explanation:
Divide 2 by 9
What word phrase can you use to represent 5x+2
Answer:
five times a number plus two.
25 Points!! :D
Complete the interphase part of the data from your data table.
Answer: you should have gotten a pic that shows all the cells phases just count the interphase ones however in the interphase cells spend 90% of its life cycle in this phase
What is the smallest two-digit integer $n$ such that switching its digits and then adding 3 results in $2n$
We can write
n = 10a + b
where a and b belong to {1, 2, 3, …, 9}.
Swapping the digits produces a new number
n' = 10b + a
and adding 3 to this number makes up 2n,
n' + 3 = 2n
or
(10b + a) + 3 = 2 (10a + b)
so that
19a - 8b = 3
Since we want n to be the smallest possible 2-digit number that meets the criteria, let's start with a = 1. Then solving for b, we find
19 - 8b = 3
16 = 8b
b = 2
So, the number we're looking for is n = 12.
Just to confirm, swapping the digits gives 21, and 21 + 3 = 24 = 2•12.
A recipe that makes 24 cupcakes calls for 5 1/2 cups of flour. How much flour is needed to make 30 cupcakes?
A. 5 7/8 cups
B. 6 1/2 cups
C. 5 3/4 cups
D. 6 7/8 cups
Answer: D hope this helps
Each of three friends Lynn Jada and Andre has the goal of raising $40 how much money did each person raise according to the following Jada raise 50% of her goal
Answer:
is it 60$
Step-by-step explanation:
because if its 100% than it would be 40+40+40
due to 50% = 120 ÷50%
= 60
Answer 1-5 for each! I’ll mark as brainiest
Answer:
4 because I had this quiz and I got 80
