Answers
The option that can be used to verify the trigonometric identity, [tex]tan\left(\dfrac{x}{2}\right)+cot\left(x \right) = csc\left(x \right)[/tex] is option C;
C. [tex]tan\left(\dfrac{x}{2} \right) + cot\left(x \right) = \dfrac{1-cos\left(x \right)}{sin\left( x \right)} +\dfrac{cos \left(x \right)}{sin\left(x \right)} =csc\left(x \right)[/tex]
What is a trigonometric identity?A trigonometric identity is an equations that consists of trigonometric functions that remain true for all values of the argument of the functions
The specified identity is presented as follows;
[tex]tan\left(\dfrac{x}{2} \right)+cot(x)=csc(x)[/tex]
The half angle formula for tangent indicates that we get;
[tex]tan\left(\dfrac{1}{2} \cdot \left(\eta \pm \theta \right) \right) = \dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}[/tex]
[tex]\dfrac{tan\left(\dfrac{1}{2} \cdot \eta \right)\pm tan\left(\dfrac{1}{2} \cdot \theta \right)}{1 \mp tan\left(\dfrac{1}{2} \cdot \eta \right)\times tan\left(\dfrac{1}{2} \cdot \theta \right)}=\dfrac{sin \left(\eta\right) \pm sin\left(\theta \right)}{cos \left(\eta \right) + cos \left(\theta \right)} = -\dfrac{cos \left(\eta\right) - cos\left(\theta \right)}{sin \left(\eta \right) \mp sin \left(\theta \right)}[/tex]
When η = 0, we get;
[tex]-\dfrac{cos \left(0\right) - cos\left(\theta \right)}{sin \left(0 \right) \mp sin \left(\theta \right)}=-\dfrac{1 - cos\left(\theta \right)}{0 \mp sin \left(\theta \right)}=\dfrac{1 - cos\left(\theta \right)}{sin \left(\theta \right)}[/tex]
Therefore;
[tex]tan\left(\dfrac{x}{2} \right)=\dfrac{1 - cos\left(x \right)}{sin \left(x \right)}[/tex]
[tex]cot\left(x \right) = \dfrac{cos(x)}{sin(x)}[/tex]
[tex]tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}[/tex]
[tex]\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1-cos(x)+cos(x)}{sin(x)} = \dfrac{1}{sin(x)}[/tex]
[tex]\dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)}=\dfrac{1}{sin(x)}=csc(x)[/tex]
Therefore;
[tex]tan\left(\dfrac{x}{2} \right)+cot(x)= \dfrac{1 - cos\left(x \right)}{sin \left(x \right)} +\dfrac{cos(x)}{sin(x)} = csc(x)[/tex]
The correct option that can be used to verify the identity is option C
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Related Questions
Please help will mark Brainly
Answers
The solutions of the equation 3x - y = 1 are (-2,-7),(-1,-4) and (3,8) thus option (A),(B) and (D) are correct.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
In another word, the equation must be constrained with some constraints.
As per the given equation,
3x - y = 1
Substitute, x = -2
3(-2) - y = 1
y = -7 thus (-2,-7) satisfied.
Similarly (-1,-4) and (3,8) are also satisfied.
Hence "The solutions of the equation 3x - y = 1 are (-2,-7),(-1,-4) and (3,8)".
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Solve the inequality for x. 10x>9(2x-5)-11
Explain what your solution means, what values would make the equation true?
Answers
Step-by-step explanation:
Solve the inequality for x.
10x > 9(2x - 5) - 11
10x > 18x - 45 - 11
10x > 18x - 56
subtract 18x from both sides:
10x - 18x > 18x - 56 - 18x
-8x > - 56
divide both sides by -8 and remember to flip the sign:
-8x/-8 < - 56/-8
x < 7
This means that x can be any number below 7.
In set builder notation: (-∞ , 7).
express 1-tan(a) as a product
Answers
The given expression 1-tan(a) is simplified as (cos(a)-sin(a))/cos(a).
The given trigonometric expression is 1-tan(a).
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
We know that, tanθ=sinθ/cosθ
Now, 1-tan(a) =1-sin(a)/cos(a)
= (cos(a)-sin(a))/cos(a)
Therefore, the given expression 1-tan(a) is simplified as (cos(a)-sin(a))/cos(a).
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8) Find the value of the term in the arithmetic sequence. (an = a₁ + (n-1)d)
27, 22, 17, 12, 7, 2,... (10th term)
a10-18
a10 = -22
a10 = -20
a10 = -21
Answers
The given term of the arithmetic sequence is -18. The correct option is (A).
What is an arithmetic sequence?An arithmetic sequence is a kind of sequence of numbers where the difference of any two consecutive terms are the same.
This difference is known as the common difference of the sequence.
The given arithmetic sequence is as below,
27, 22, 17, 12, 7, 2,...
Since the nth term of an arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
Where d is the common difference.
The common difference for the given sequence is,
d = 22 - 27
= -5
Substitute d = -5 and n = 10 in the general form of nth term to obtain,
a₁₀ = a₁ + (n - 1)d
= 27 + -5(10 - 1)
= 27 - 45
= -18
Hence, the value of the 10th term of the given sequence is -18.
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find the simple interesr on ₹20000 for 4 ¹/2 years at 8¹/2% per anum
Answers
Answer:
7650 rupees
Step-by-step explanation:
Use I = Pnr
Here P = Principal = 20000 rupees
n = time = 4.5 years
r = rate of interest = 8.5% = 8.5/100
Alright! I have two more questions! Please give an explanation of how to get x ,y, and z! Thanks!
Answers
Using the definition of isosceles and equilateral triangles:
12. x = 77°; y = 58°; z = 122°
13. x = 60°; y = 120°; z = 60°
What are Equilateral and Isosceles Triangles?All three sides and angles of an equilateral triangle are equal in measure. On the other hand, two sides and two base angles of an isosceles triangle are equal to each other.
12. x = 1/2(180 - 26) [based on the definition of isosceles triangle]
x = 1/2(154)
x = 77°
y = 1/2(180 - (90 - 26)) [based on the definition of isosceles triangle]
y = 1/2(180 - 64)
y = 1/2(116)
y = 58°
z = 180 - 58 [base angles of isosceles triangle are equal]
z = 122°
13. Each interior angle of an equilateral triangle is equal to 60 degrees.
Therefore, x = the measure of one interior angle
x = 60°
y = 180 - 60 [linear pair]
y = 120°
The base angles of the triangle that has two equal sides would be 60° [180 - 120]
Therefore:
z = 180 - 2(60)
z = 60°
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A rectangular garage has a perimeter of 46 meters and an area of 130 square meters. What are the dimensions of the garage?
Answers
The length of the rectangular garage will be 13 while the width will be 10.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
The perimeter of the rectangle = 2( length + width).
It is known that,
Area of rectangle = length × width.
130 = L× W
L = 130/W
The perimeter of the rectangle = 2( length + width).
46= 2( L+ W)
L + W = 23
130/W + W = 23
130 + W² = 23W
W² - 23W + 130 = 0
W² -13W - 10W + 130 = 0
W(W - 13) -10(W - 13) = 0
(W - 13)(W - 10) = 0
W = 13,10
For W = 13
L = 23 - 13 = 10
For W = 10
L = 23 - 10 = 13
Let's say the bigger dimension is the length and the smaller is the width.
Length = 13 and Width = 10
Hence "The length of the rectangular garage will be 13 while the width will be 10".
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Andrea can type 15 words per minute. If she types for 7 minutes, how many
words did she type?
Answers
Answer: 105 words
Step-by-step explanation:
15x7=105
If in 1 minute she can type 15 words, then you would have to multiply 15 with 7 to get 105 words in 7 minutes
The first angle in a triangle is three times that of a second angle. The second angle is two times that of the third angle. Find the ratio of the angles in the triangle.
Answers
The first angle in a triangle is three times that of a second angle. The second angle is two times that of the third angle. The ratio of the angles in the triangle is 1:2:3.
Define angle.When two rays are joined at one point, they produce the geometric shape known as an angle. The vertex is the shared point between the two rays, which are known as the arms or sides of the angle. When two rays meet at a point, they make an angle. An "angle" is the term used to describe the "opening" between these two rays, and it is symbolised by the symbol. Angles are typically expressed as 60°, 90°, etc. and are measured in degrees.
Given,
A first angle of let x
2x = 2nd angle
3x = 3rd angle
Angle sum = 180
x + 2x + 3x = 180
6x = 180
Dividing,
x = 30°
2x = 2(30)
2nd angle = 60
3x = 3(30)
3rd angle = 90
30°, 60°, and 90° are the three angles.
Ratio 1:2:3
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Evaluate the expression for the given values. If a=3 and b=−6, find a−b2.
Answers
Answer:
-33
Step-by-step explanation:
just fill in the values
3-6^2
3-36
-33
Hopes this helps please mark brainliest
Answer:
-33
Step-by-step explanation:
a = 3; b = -6
a - b² = 3 - (-6)² = 3 - 36 = -33
POLIGONOS: si tengo de informacion que 360 entre n es igual a 72 como puedo saber cual es el angulo interno la suma de angulos interno y el nombre del poligono?
Answers
El polígono regular tiene las características de un pentágono, cuya medida de ángulo central es 72° y la suma de todos los ángulos centrales es igual a 360°.
¿Qué polígono tiene un ángulo central de 72 grados?
En este problema debemos determinar que polígono regular tiene un ángulo central con medida de 72°, la suma de todos los ángulos centrales de un polígono es igual a 360°. El número de lados del polígono se puede determinar mediante la siguiente operación:
n = 360° / θ
Donde θ es la medida del ángulo central, en grados.
Si sabemos que θ = 72°, entonces el número de lados del polígono:
n = 360° / 72°
n = 5
El polígono regular es un pentágono.
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Please answer fast will give 100 point things.
QUESTION BELOW
I WILL REPORT TROLLS!
THANK YOU
Answers
Answer:
A. 56
Step-by-step explanation:
Let the three consecutive integers be:
xx + 1x + 2Given:
The sum of three consecutive integers is 30 more than twice the smallest integer.Create an equation with the given information and solve for x:
[tex]\implies x+(x+1)+(x+2)=2x+30[/tex]
[tex]\implies 3x+3=2x+30[/tex]
[tex]\implies 3x+3-2x=2x+30-2x[/tex]
[tex]\implies x+3=30[/tex]
[tex]\implies x+3-3=30-3[/tex]
[tex]\implies x=27[/tex]
Therefore, the three consecutive integers are:
27, 28 and 29.So the sum of the first and last integer is:
[tex]\implies 27+29=56[/tex]
Answer:
a) 56 --- (27, 28, 29)
Step-by-step explanation:
Forming the equation,
→ x + (x + 1) + (x + 2) = 2x + 30
Now the value of x will be,
→ x + (x + 1) + (x + 2) = 2x + 30
→ x + x + 1 + x + 2 = 2x + 30
→ 3x - 2x = 30 - 3
→ [ x = 27 ]
The last integer will be,
→ x + 2
→ 27 + 2 = 29
Sum of first and last integer is,
→ x + (x + 2)
→ 27 + (27 + 2)
→ 27 + 29 = 56
Hence, required answer is 56.
PLEASE HELP!!
solve for substitution
y+4=x
10x+2y+16
Answers
Using the substitution the system of equations y + 4 = x and 10x + 2y + 16 is solved to be
x = 8/3y = -4/3How to solve the system of equationsSubstitution involves replacing a value with it's equal
The given equation include
y + 4 = x
10x + 2y + 16
substituting x = y + 4 into 10x + 2y + 16
10x + 2y + 16
= 10(y + 4) + 2y + 16
= 10y + 40 + 2y + 16
collecting like terms
= 12y + 16
12y = -16
y = -16/12
y = -4/3
substituting y = -4/3 into x = y + 4
x = -4/3 + 4
x = 8/3
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What is the approximate circumference of the circle shown below
Answers
Answer:
Approximately 51.21 cm
Step-by-step explanation:
to find circumference we multiply the diameter by pi
16.3pi
51.21 cm
Hopes this helps please mark brainliest
Answer:
C = 51.182 cm
Step-by-step explanation:
The circumference is given by
C = pi * d where d is the diameter
C = pi * 16.3
C = 16.3 pi
We can approximate pi by 3.14
C = 16.3 * 3.14
C = 51.182 cm
Determine a series of transformations that would map Figure I onto Figure J.
A blank followed by a blank
Answers
The series of transformations that would map Figure M onto Figure N will be firstly rotated about the origin and then translated upward by 3 units.
What is a transformation of a shape?
A point, line, or geometric figure can be transformed in one of four ways, each of which affects the structure and/or location of the object.
From before the refers to the object's initial condition, and Picture, after transformation, refers to the object's ultimate structure and location.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
If the geometry is rotated, then there is no change in angles.
The translation does not change the shape and size of the geometry. But changes the location.
The series of transformations that would map Figure M onto Figure N will be firstly rotated about the origin and then translated upward by 3 units.
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Disclaimer
The question given by you is incomplete, so a similar question have been solved here and the image is attached.
Determine a series of transformations that would map Figure M onto Figure N.
Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the equation.
(3,−2); y=x+4
Answers
Answer:
y= -x+1
Step-by-step explanation:
The slope of a line that is perpendicular to a graph is equal to the negative reciprocal of the graph's slope.
slope = 1 negative reciprocal = - (1/1) = -1
Now, you have to find the y-intercept by using the given points (3,-2) and the slope that was found (-x)
y= -x+b
-2=-3+b
1=b
y= -x+1
Draw your own face using the grid below and write down the coordinates of the outline
Answers
Answer:
Step-by-step explanation:
You need a take a picture so I know what question your talking about
I need help asap thank you...
Answers
The Vertical opposite angles are ∠1 = 141° ; ∠2 = 39° ; ∠3 = 141° ; ∠4 =39°
The given angle cover the whole circle which will have 360°
∠1 + ∠2 +∠3 + ∠4 = 360°
∠1 + 39° +∠3 + ∠4 = 360°
Vertically Opposite angle:
The angles formed opposite to each other by a transversal. Horizontal Angles (Vertically Opposite Angles)The opposing angles created by the junction of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another are always equal.Hence, ∠1 = ∠3 and ∠2 = ∠4. So ∠4 = 39°
∠1 + 39° +∠3 + 39° = 360°
Let x be the ∠1 and ∠3;
x + 39° +x + 39° = 360°
2x = 360° - 78°
2x = 282°
x = 141°
Now, we know all the angles with respect to Vertical opposite Angles .
∠1 = 141°
∠2 = 39°
∠3 = 141°
∠4 =39°
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Match each equation with the inverse operation you should use (on both sides of the equation) to solve for x.
x + 2 = 10 _____
x - 2 = 10 ____
2x = 10 ____
x/2 = 10 ____
Answers
x + 2 = 10
x + 2 - 2 = 10 - 2
x = 8
x - 2 = 10
x - 2 + 2 = 10 + 2
x = 12
2x = 10
2x/2 = 10/2
x = 5
x/2 = 10
x/2 × 2 = 10 × 2
x = 20
I HOPE IT HELPS EVEN THOUGH YOUR ANSWER TO MY QUESTION IS JUST A NONSENSE.Which function has a greater y-intercept? f(x)=1/3x+1/2
Answers
Answer:
f(x)
Step-by-step explanation:
the function g(x) has y-interception in point (0;0), the function f(x) has y-interception in point (0; 1/3). For more details see the attachment.
What number of inches is equivalent to 848
Answers
not defined because 848 has no unit
Write the equation of the linear relationship in slope-intercept form.
The equation that represents this relationship is y =
(select)
Answers
Answer:
Number 2
Step-by-step explanation:
can someone help me with these questions??? ill give 45 points
1. 5 miles in 1 1/2
2. 2/3 pound for every 1/4 tablespoon
3. 6 pages every 1/5 hour
Marcus can type 40 words in half a minute. Rhys can type 100 words in one and a half minutes. Which student can type at a greater rate of words per minute?
Answers
The student who can write more words per minute is Marcus because he writes at a speed of 1.3 words per second, that is, in one minute he writes 79.8 words while Rhys writes at a speed of 1.1 words per second and in one minute he writes 66.66 words.
How to identify which student writes faster?To identify the speed at which students write we must divide the number of words the student writes in time (seconds) as shown below.
Marcus
40 words / 30 seconds = 1.33Rhys
100 words / 90 seconds = 1.11Using the information above, we need to multiply the number of words each student types per second by the number of seconds that equals one minute.
1 minute = 60 secondsRhys
1.11 * 60 seconds = 66.6Marcus
1.33 * 60 seconds = 79.8According to the information above, Marcus has a faster typing speed than Rhys because he types 79.8 words in one minute, while Rhys types 66.6 words in the same time.
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U
?
120°
R
V
STIMOH
50°
22A.J3
Find the measure of the indicated angle in the
drawing above.
Answers
The measure of angle VUT is ∠VUT = 70°.
What are angles in a linear pair?
When two lines intersect at a single point, a linear pair of angles is formed. If the angles are adjacent to each other after the two lines intersect, they are said to be linear. The sum of the angles of a linear pair is always 180°. These angles are also referred to as supplementary angles.
In the given figure, ∠RVU and ∠UVT are in linear pair, so by using the property of angles in a linear pair, we can write
∠RVU + ∠UVT = 180°
120° + ∠UVT = 180°
∠UVT = 60°
Now as we know the sum of all angles of a triangle is equal to 180°,
∠UVT + ∠VTU + ∠VUT = 180°.
60° + 50° + ∠VUT =180°
110° + ∠VUT = 180°
∠VUT = 180° - 110°
∠VUT = 70°
Hence, the measure of angle VUT is ∠VUT = 70°.
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Find the circumference of each of the following circles. Use 22 for TT.
22 cm
7 in
40 mi
15 yd
Answers
Answer:
A) [tex]\frac{484}{7}[/tex]cm
B)[tex]44[/tex]in
C)[tex]\frac{880}{7}[/tex]mi
D)[tex]\frac{660}{7}[/tex]yd
Step-by-step explanation:
The formula for the circumference of a circle is:
[tex]C=2\pi r[/tex]
Within the problem it is stated to use [tex]\frac{22}{7}[/tex] for [tex]\pi[/tex] so our equation will be:
[tex]C=2\frac{22}{7}r[/tex] which simplifies to [tex]C=\frac{44r}{7}[/tex]
The variable [tex]r[/tex] in the equation for the circumference represents 'radius' which is half the diameter, for circle's A and C we are given a diameter. We can divide these numbers in half to get a radius. From there we plug in each radius to get circumference of each circle!
A)
[tex]\text{Diameter}=22\\\text{Radius {\it (r)}}=\frac{\textit{diameter}}{2}=\frac{22}{2}=11\\\text{Circumference}=\frac{44(11)}{7}=\frac{484}{7}[/tex]
B)
[tex]\text{Radius {\it (r)}}=7\\\text{Circumference}=\frac{44(7)}{7}=\frac{308}{7}=44[/tex]
C)
[tex]\text{Diameter}=40\\\text{Radius {\it (r)}}=\frac{\textit{diameter}}{2}=\frac{40}{2}=20\\\text{Circumference}=\frac{44(20)}{7}=\frac{880}{7}[/tex]
D)
[tex]\text{Radius {\it (r)}}=15\\\text{Circumference}=\frac{44(15)}{7}=\frac{660}{7}[/tex]
Remember to include units of measurement in your answers.
31
A straight line
has gradient 6
and
passes through the point (3, 19)
Work out the equation of the line.
Give your answer in the form
y = mx + c
Answers
y = 6x + 1 is the line of the equation which has a gradient of 6 and passes through the point (3, 19)
What is a gradient?
A straight line's steepness can be determined by looking at its gradient. A line's gradient does not have to be a whole integer and might be positive or negative. A line's gradient can either be uphill (positive value) or downward (negative value).
Here, we have
Equation of line
y = mx + c
m = Slope of line = Gradient = 6
= y = 6x + c
a line passes through (3, 19)
so, we find the value of c
= 19 = 6(3) + c
= c = 1
Now, we put the value of c in the equation and we get
= y = 6x + 1
Hence,y = 6x + 1 is the line of the equation which has a gradient of 6 and passes through the point (3 19)
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Evaluate the exponential function f(x)=(1/8)^-x
Answers
The exponential function f(x)=(1/8)^-x can be evaluated to give us:
f(2)= 64f(-3)= 1/512f(-3)= [tex]\frac{1}{\sqrt{\frac{1}{8} } }[/tex]What is exponential function?An exponential function serves as Mathematical function in the form f (x) = ax hving “x” as variable,the conceptis the concept of exponential function.
The given function is f(x)=(1/8)^-x
Then f(2)=(1/8)^-2 = 1/(1/8)^2 =1/(1/64) =64
f(-3)=(1/8)^-(-3) = 1/512
f(-3)=(1/8)^-(1/2) =[tex]\frac{1}{\sqrt{\frac{1}{8} } }[/tex]
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Characteristics: R:-2.5 ≤ y ≤ 7.5
minimum at x=200°
period is 270°
A) Sketch 2 cycles of the function.
Note: Remember to label the 5 main coordinates of each cycle, and the equation of axis.
B) Develop 2 equation based on the sketch above, and explain/show how you figured out each part of the equation:
(i) cosine function (in radians)
(ii) negative sine function (in degrees)
Answers
The cosine and sine functions are presented as follows;
(a) cosine function is; f(x) = 5·cos((4/3)·x - (13·π/27)) + 2.5
(b) f(x) = -5·sin((4/3)·x - 530/3) + 2.5
What is a sine function?A sine function is a periodic function used bases on the sine of an angle.
(a) The cosine function is f(x) = a·cos(b·x - c) + k
Where;
a = The amplitude
The amplitude = (Max - Min)/2
Therefore;
a = (7.5 - (-2.5))/2 = 5
f = b/(2·π)
c = The phase shift
k = The vertical shift
The minimum is at x = 200° = (200/360)·(2·π) = 10·π/9
The period = 270° = 3·π/2
Frequency, f = 2/(3·π)
b = 2·π·f = 2·π×2/(3·π) = 4/3
When the function is at the minimum point, θ = π
Therefore;
(4/3)×(10·π)/9 - c = π
c = 13·π/27
k = The minimum value + a
Therefore, k = -2.5 + 5 = 2.5
The cosine function is therefore;
f(x) = 5·cos((4/3)·x - (13·π/27)) + 2.5
(b) The negative sine function is found as follows;
f(x) = a·sin(b·x - c) + k
b = 4/3
k = 2.5
Minimum point sin((4/3)200 - c) = 180
((4/3)200 - c) = 180
c = 260/3
Using a negative sign function, we get;
((4/3)200 - c) = 90
c = 530/3
The equation is therefore;
f(x) = -5·sin((4/3)·x -530/3) + 2.5
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Answer:
simplify 8/6, and you get 4/3.
This is a coincidence, because this is a Pythagorean triple,
which means: opp = 4, adj = 3, hyp = 5
now, we can solve the rest easily
sin(0) = 4/5
cos(0) = 3/5
sec = 5/3 (opposite of cos)
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The cos, tan, sec, csc and cot of the angle θ in quadrant IV are 3/5, -4/3, 5/3, -5/4 and -3/4 respectively
How to find the trigonometric ratio of the angle?
Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Given that: sin(θ) = -4/5 and θ is in quadrant 4.
Using this information, we can sketch the location of the angle θ in the quadrant (See the attached image). Therefore:
(a) cos(θ) = 3/5 (adj/hyp)
(b) tan(θ) = -4/3 (opp/adj)
(c) sec(θ) = 1/cos(θ) = 5/3
(d) csc(θ) = 1/sin(θ) = -5/4
(e) cot(θ) = 1/tan(θ) = -3/4
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