# 7.4 The other trigonometric functions  (Page 8/14)

 Page 8 / 14

Find the area of the sector of a circle with diameter 32 feet and an angle of $\text{\hspace{0.17em}}\frac{3\pi }{5}\text{\hspace{0.17em}}$ radians.

For the following exercises, find the angle between $\text{\hspace{0.17em}}0°\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\text{360°}\text{\hspace{0.17em}}$ that is coterminal with the given angle.

$420°$

$60°$

$-80°$

For the following exercises, find the angle between 0 and $\text{\hspace{0.17em}}2\pi \text{\hspace{0.17em}}$ in radians that is coterminal with the given angle.

$-\text{\hspace{0.17em}}\frac{20\pi }{11}$

$\frac{2\pi }{11}$

$\frac{14\pi }{5}$

For the following exercises, draw the angle provided in standard position on the Cartesian plane.

$-210°$

$75°$

$\frac{5\pi }{4}$

$-\frac{\pi }{3}$

Find the linear speed of a point on the equator of the earth if the earth has a radius of 3,960 miles and the earth rotates on its axis every 24 hours. Express answer in miles per hour. Round to the nearest hundredth.

1036.73 miles per hour

A car wheel with a diameter of 18 inches spins at the rate of 10 revolutions per second. What is the car's speed in miles per hour? Round to the nearest hundredth.

## Right Triangle Trigonometry

For the following exercises, use side lengths to evaluate.

$\mathrm{cos}\text{\hspace{0.17em}}\frac{\pi }{4}$

$\frac{\sqrt{2}}{2}$

$\mathrm{cot}\text{\hspace{0.17em}}\frac{\pi }{3}$

$\mathrm{tan}\text{\hspace{0.17em}}\frac{\pi }{6}$

$\frac{\sqrt{3}}{3}$

$\mathrm{cos}\left(\frac{\pi }{2}\right)=\mathrm{sin}\left(___°\right)$

$\mathrm{csc}\left(18°\right)=\mathrm{sec}\left(___°\right)$

$72°$

For the following exercises, use the given information to find the lengths of the other two sides of the right triangle.

$\mathrm{cos}\text{\hspace{0.17em}}B=\frac{3}{5},a=6$

$\mathrm{tan}\text{\hspace{0.17em}}A=\frac{5}{9},b=6$

$a=\frac{10}{3},c=\frac{2\sqrt{106}}{3}$

For the following exercises, use [link] to evaluate each trigonometric function.

$\mathrm{tan}\text{\hspace{0.17em}}B$

$\frac{6}{11}$

For the following exercises, solve for the unknown sides of the given triangle.

$a=\frac{5\sqrt{3}}{2},b=\frac{5}{2}$

A 15-ft ladder leans against a building so that the angle between the ground and the ladder is $\text{\hspace{0.17em}}70°.\text{\hspace{0.17em}}$ How high does the ladder reach up the side of the building? Find the answer to four decimal places.

The angle of elevation to the top of a building in Baltimore is found to be 4 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building. Find the answer to four decimal places.

369.2136 ft

## Unit Circle

Find the exact value of $\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\frac{\pi }{3}.$

Find the exact value of $\text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}\frac{\pi }{4}.$

$\frac{\sqrt{2}}{2}$

Find the exact value of $\text{\hspace{0.17em}}\mathrm{cos}\text{\hspace{0.17em}}\pi .$

State the reference angle for $\text{\hspace{0.17em}}300°.\text{\hspace{0.17em}}$

$60°$

State the reference angle for $\text{\hspace{0.17em}}\frac{3\pi }{4}.$

Compute cosine of $\text{\hspace{0.17em}}330°.$

$\frac{\sqrt{3}}{2}$

Compute sine of $\text{\hspace{0.17em}}\frac{5\pi }{4}.$

State the domain of the sine and cosine functions.

all real numbers

State the range of the sine and cosine functions.

## The Other Trigonometric Functions

For the following exercises, find the exact value of the given expression.

$\mathrm{cos}\text{\hspace{0.17em}}\frac{\pi }{6}$

$\frac{\sqrt{3}}{2}$

$\mathrm{tan}\text{\hspace{0.17em}}\frac{\pi }{4}$

$\mathrm{csc}\text{\hspace{0.17em}}\frac{\pi }{3}$

$\frac{2\sqrt{3}}{3}$

$\mathrm{sec}\text{\hspace{0.17em}}\frac{\pi }{4}$

For the following exercises, use reference angles to evaluate the given expression.

$\mathrm{sec}\text{\hspace{0.17em}}\frac{11\pi }{3}$

2

$\mathrm{sec}\text{\hspace{0.17em}}315°$

If $\text{\hspace{0.17em}}\mathrm{sec}\left(t\right)=-2.5,$ what is the $\text{\hspace{0.17em}}\text{sec}\left(-t\right)?$

–2.5

If $\text{\hspace{0.17em}}\text{tan}\left(t\right)=-0.6,$ what is the $\text{\hspace{0.17em}}\text{tan}\left(-t\right)?$

If $\text{\hspace{0.17em}}\text{tan}\left(t\right)=\frac{1}{3},$ find $\text{\hspace{0.17em}}\text{tan}\left(t-\pi \right).$

$\frac{1}{3}$

If $\text{\hspace{0.17em}}\text{cos}\left(t\right)=\frac{\sqrt{2}}{2},$ find $\text{\hspace{0.17em}}\text{sin}\left(t+2\pi \right).$

Which trigonometric functions are even?

cosine, secant

Which trigonometric functions are odd?

## Chapter practice test

Convert $\text{\hspace{0.17em}}\frac{5\pi }{6}\text{\hspace{0.17em}}$ radians to degrees.

$150°$

Convert $\text{\hspace{0.17em}}-620°\text{\hspace{0.17em}}$ to radians.

Find the length of a circular arc with a radius 12 centimeters subtended by the central angle of $\text{\hspace{0.17em}}30°.$

6.283 centimeters

Find the area of the sector with radius of 8 feet and an angle of $\text{\hspace{0.17em}}\frac{5\pi }{4}\text{\hspace{0.17em}}$ radians.

Find the angle between $\text{\hspace{0.17em}}0°\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\text{360°}\text{\hspace{0.17em}}$ that is coterminal with $\text{\hspace{0.17em}}375°.$

$15°$

Find the angle between 0 and $\text{\hspace{0.17em}}2\pi \text{\hspace{0.17em}}$ in radians that is coterminal with $\text{\hspace{0.17em}}-\frac{4\pi }{7}.$

Draw the angle $\text{\hspace{0.17em}}315°\text{\hspace{0.17em}}$ in standard position on the Cartesian plane.

Draw the angle $\text{\hspace{0.17em}}-\frac{\pi }{6}\text{\hspace{0.17em}}$ in standard position on the Cartesian plane.

A carnival has a Ferris wheel with a diameter of 80 feet. The time for the Ferris wheel to make one revolution is 75 seconds. What is the linear speed in feet per second of a point on the Ferris wheel? What is the angular speed in radians per second?

3.351 feet per second, $\text{\hspace{0.17em}}\frac{2\pi }{75}\text{\hspace{0.17em}}$ radians per second

Find the missing sides of the triangle $\text{\hspace{0.17em}}ABC:\mathrm{sin}\text{\hspace{0.17em}}B=\frac{3}{4},c=12.$

Find the missing sides of the triangle.

$a=\frac{9}{2},b=\frac{9\sqrt{3}}{2}$

The angle of elevation to the top of a building in Chicago is found to be 9 degrees from the ground at a distance of 2000 feet from the base of the building. Using this information, find the height of the building.

Find the exact value of $\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\frac{\pi }{6}.$

$\frac{1}{2}$

Compute sine of $\text{\hspace{0.17em}}240°.$

State the domain of the sine and cosine functions.

real numbers

State the range of the sine and cosine functions.

Find the exact value of $\text{\hspace{0.17em}}\mathrm{cot}\text{\hspace{0.17em}}\frac{\pi }{4}.$

1

Find the exact value of $\text{\hspace{0.17em}}\mathrm{tan}\text{\hspace{0.17em}}\frac{\pi }{3}.$

Use reference angles to evaluate $\text{\hspace{0.17em}}\mathrm{csc}\text{\hspace{0.17em}}\frac{7\pi }{4}.$

$\text{\hspace{0.17em}}-\sqrt{2}$

Use reference angles to evaluate $\text{\hspace{0.17em}}\mathrm{tan}\text{\hspace{0.17em}}210°.$

If $\text{\hspace{0.17em}}\text{csc}\text{\hspace{0.17em}}t=0.68,$ what is the $\text{\hspace{0.17em}}\text{csc}\left(-t\right)?$

–0.68

If $\text{\hspace{0.17em}}\text{cos}\text{\hspace{0.17em}}t=\frac{\sqrt{3}}{2},$ find $\text{\hspace{0.17em}}\text{cos}\left(t-2\pi \right).$

Find the missing angle: $\text{\hspace{0.17em}}\mathrm{cos}\left(\frac{\pi }{6}\right)=\mathrm{sin}\left(___\right)$

$\frac{\pi }{3}$

#### Questions & Answers

x exposant 4 + 4 x exposant 3 + 8 exposant 2 + 4 x + 1 = 0
HERVE Reply
x exposent4+4x exposent3+8x exposent2+4x+1=0
HERVE
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find to nearest one decimal place of centimeter the length of an arc of circle of radius length 12.5cm and subtending of centeral angle 1.6rad
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factoring polynomial
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find general solution of the Tanx=-1/root3,secx=2/root3
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0.75
Lynne
0.75
Inkoom
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duru Reply
depending on the question
Nicholas
I am a carpenter and I have to cut and assemble a conventional roof line for a new home. The dimensions are: width 30'6" length 40'6". I want a 6 and 12 pitch. The roof is a full hip construction. Give me the L,W and height of rafters for the hip, hip jacks also the length of common jacks.
John
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about complex fraction
Raihany
Hello
Cromwell
a
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x-39=72 x=111
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Solve the formula for the indicated variable P=b+4a+2c, for b
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Need help with this question please
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b=-4ac-2c+P
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b=p-4a-2c
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b= p - 4a - 2c
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p=2(2a+C)+b
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A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 30 days, is given by g(x)=250,000csc(π30x). Graph g(x) on the interval [0, 35]. Evaluate g(5)  and interpret the information. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? Find and discuss the meaning of any vertical asymptotes.
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The sequence is {1,-1,1-1.....} has
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