<< Chapter < Page Chapter >> Page >

Find the area of the sector of a circle with diameter 32 feet and an angle of 3 π 5 radians.

Got questions? Get instant answers now!

For the following exercises, find the angle between and 360° that is coterminal with the given angle.

For the following exercises, find the angle between 0 and 2 π in radians that is coterminal with the given angle.

20 π 11

2 π 11

Got questions? Get instant answers now!

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

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

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

Right Triangle Trigonometry

For the following exercises, use side lengths to evaluate.

cos ( π 2 ) = sin ( ___° )

Got questions? Get instant answers now!

csc ( 18° ) = sec ( ___° )

72°

Got questions? Get instant answers now!

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

tan A = 5 9 , b = 6

a = 10 3 , c = 2 106 3

Got questions? Get instant answers now!

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

A right triangle with side lengths of 11 and 6. Corners A and B are also labeled.  The angle A is opposite the side labeled 11.  The angle B is opposite the side labeled 6.

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

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Unit Circle

Find the exact value of sin π 3 .

Got questions? Get instant answers now!

Find the exact value of cos π 4 .

2 2

Got questions? Get instant answers now!

Find the exact value of cos π .

Got questions? Get instant answers now!

State the reference angle for 300° .

60°

Got questions? Get instant answers now!

State the reference angle for 3 π 4 .

Got questions? Get instant answers now!

Compute cosine of 330° .

3 2

Got questions? Get instant answers now!

Compute sine of 5 π 4 .

Got questions? Get instant answers now!

State the domain of the sine and cosine functions.

all real numbers

Got questions? Get instant answers now!

State the range of the sine and cosine functions.

Got questions? Get instant answers now!

The Other Trigonometric Functions

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

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

If sec ( t ) = −2.5 , what is the sec ( t ) ?

–2.5

Got questions? Get instant answers now!

If tan ( t ) = −0.6 , what is the tan ( t ) ?

Got questions? Get instant answers now!

If tan ( t ) = 1 3 , find tan ( t π ) .

1 3

Got questions? Get instant answers now!

If cos ( t ) = 2 2 , find sin ( t + 2 π ) .

Got questions? Get instant answers now!

Which trigonometric functions are even?

cosine, secant

Got questions? Get instant answers now!

Which trigonometric functions are odd?

Got questions? Get instant answers now!

Chapter practice test

Convert 5 π 6 radians to degrees.

150°

Got questions? Get instant answers now!

Convert −620° to radians.

Got questions? Get instant answers now!

Find the length of a circular arc with a radius 12 centimeters subtended by the central angle of 30° .

6.283 centimeters

Got questions? Get instant answers now!

Find the area of the sector with radius of 8 feet and an angle of 5 π 4 radians.

Got questions? Get instant answers now!

Find the angle between and 360° that is coterminal with 375° .

15°

Got questions? Get instant answers now!

Find the angle between 0 and 2 π in radians that is coterminal with 4 π 7 .

Got questions? Get instant answers now!

Draw the angle 315° in standard position on the Cartesian plane.


This is an image of a graph of a circle with an angle inscribed.

Got questions? Get instant answers now!

Draw the angle π 6 in standard position on the Cartesian plane.

Got questions? Get instant answers now!

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, 2 π 75 radians per second

Got questions? Get instant answers now!

Find the missing sides of the triangle A B C : sin B = 3 4 , c = 12.

Got questions? Get instant answers now!

Find the missing sides of the triangle.


A right triangle with hypotenuse length of 9 and angle measure of 60 degrees.

a = 9 2 , b = 9 3 2

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

Find the exact value of sin π 6 .

1 2

Got questions? Get instant answers now!

Compute sine of 240° .

Got questions? Get instant answers now!

State the domain of the sine and cosine functions.

real numbers

Got questions? Get instant answers now!

State the range of the sine and cosine functions.

Got questions? Get instant answers now!

Find the exact value of cot π 4 .

1

Got questions? Get instant answers now!

Find the exact value of tan π 3 .

Got questions? Get instant answers now!

Use reference angles to evaluate csc 7 π 4 .

2

Got questions? Get instant answers now!

Use reference angles to evaluate tan 210° .

Got questions? Get instant answers now!

If csc t = 0.68 , what is the csc ( t ) ?

–0.68

Got questions? Get instant answers now!

If cos t = 3 2 , find cos ( t 2 π ) .

Got questions? Get instant answers now!

Find the missing angle: cos ( π 6 ) = sin ( ___ )

π 3

Got questions? Get instant answers now!

Questions & Answers

the third and the seventh terms of a G.P are 81 and 16, find the first and fifth terms.
Suleiman Reply
if a=3, b =4 and c=5 find the six trigonometric value sin
Martin Reply
pls how do I factorize x⁴+x³-7x²-x+6=0
Gift Reply
in a function the input value is called
Rimsha Reply
how do I test for values on the number line
Modesta Reply
if a=4 b=4 then a+b=
Rimsha Reply
a+b+2ab
Kin
commulative principle
DIOSDADO
a+b= 4+4=8
Mimi
If a=4 and b=4 then we add the value of a and b i.e a+b=4+4=8.
Tariq
what are examples of natural number
sani Reply
an equation for the line that goes through the point (-1,12) and has a slope of 2,3
Katheryn Reply
3y=-9x+25
Ishaq
show that the set of natural numberdoes not from agroup with addition or multiplication butit forms aseni group with respect toaaddition as well as multiplication
Komal Reply
x^20+x^15+x^10+x^5/x^2+1
Urmila Reply
evaluate each algebraic expression. 2x+×_2 if ×=5
Sarch Reply
if the ratio of the root of ax+bx+c =0, show that (m+1)^2 ac =b^2m
Awe Reply
By the definition, is such that 0!=1.why?
Unikpel Reply
(1+cosA+IsinA)(1+cosB+isinB)/(cos@+isin@)(cos$+isin$)
Ajay Reply
hatdog
Mark
jaks
Ryan
how we can draw three triangles of distinctly different shapes. All the angles will be cutt off each triangle and placed side by side with vertices touching
Shahid Reply
Practice Key Terms 6

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask