Question 1

(a) Convert $-240^{\circ}$ to radians.
(b) Convert $\frac{7 \pi}{15}$ to degrees.

Accepted Answer

(a) $-\frac{4 \pi}{3}$
(b) $84^{\circ}$

Question 2

A wheel is turning at a speed of 200 revolutions per minute. Through how many degrees does a point on the edge of the wheel move in 1.5 seconds?

Accepted Answer

$1800^{\circ}$

Question 3

Find the angle of smallest positive measure coterminal with $-418^{\circ}$.

Accepted Answer

$302^{\circ}$

Question 4

A central angle of a circle with radius 50 centimeters cuts off an arc of 120 centimeters. Find each measure.
(a) The radian measure of the angle.
(b) The area of the sector with this central angle.

Accepted Answer

The answer of A central angle of a circle with...

Question 5

Find the length of an arc intercepted by an angle of $60^{\circ}$ in a circle with radius 15 inches.

Accepted Answer

The answer of Find the length of an arc intercepted...

Question 6

graph the given function over a two-period interval. Identify asymptotes when applicable.
-$y=\tan (x-\pi)$

Accepted Answer

The answer of graph the given function over a two-period...

Question 7

graph the given function over a two-period interval. Identify asymptotes when applicable.
-$y=-\sin 4 x$

Accepted Answer

The answer of graph the given function over a two-period...

Question 8

graph the given function over a two-period interval. Identify asymptotes when applicable.
-$y=2 \sin \left(x+\frac{\pi}{2}\right)+1$

Accepted Answer

The answer of graph the given function over a two-period...

Question 9

graph the given function over a two-period interval. Identify asymptotes when applicable.
-The average monthly low temperature (in $\mathrm{F}^{\circ}$ ) in London can be modeled using the trigonometric function defined by $f(x)=10 \sin \left[\frac{\pi}{6}(x-4.2)\right]+46$, where $x$ is the month and $x=1$ corresponds to January.
(a) Graph $f$ over the interval $1 \leq x \leq 25$.
(b) Determine the amplitude, period, phase shift, and vertical translation of $f$.
(c) What is the average monthly low temperature for the month of October?
(d) Find the maximum and minimum average monthly low temperatures and the months when they occur.
(e) What would be an approximation for the average yearly low temperature in London? How is this related to the vertical translation of the sine function in the formula for $f$ ?

Accepted Answer

The answer of graph the given function over a two-period...

Question 10

If $\cos \theta<0$ and $\tan \theta>0$, in which quadrant does $\theta$ lie?

Accepted Answer

The answer of If $\cos \theta<0$ and $\tan \theta>0$, in...

Question 11

Use the figure to find the following:
  
(a) The smallest positive angle coterminal with $\theta$.
(b) The values of $x$ and $y$.
(c) The values of the six trigonometric functions of $\theta$.
(d) The radian measure of $\theta$.

Accepted Answer

The answer of Use the figure to find the following:
...

Question 12

If $(-3,4)$ is on the terminal side of an angle $\theta$ in standard position, find $\sin \theta, \cos \theta$, and $\tan \theta$.

Accepted Answer

The answer of If $(-3,4)$ is on the terminal side...

Question 13

If $\sin \theta=\frac{3}{5}$ and $\theta$ is in quadrant II find the values of the other trigonometric functions of $\theta$.

Accepted Answer

The answer of If $\sin \theta=\frac{3}{5}$ and $\theta$ is in...

Question 14

Find the exact values of each part labeled with a letter.

Accepted Answer

The answer of Find the exact values of each part...

Question 15

Find the exact value of $\cot \left(-480^{\circ}\right)$.

Accepted Answer

The answer of Find the exact value of $\cot \left(-480^{\circ}\right)$....

Question 16

Use a calculator to approximate the following.
(a) $\cos 28^{\circ} 52^{\prime}$
(b) $\cot 52.1896^{\circ}$
(c) $\csc 19.635^{\circ}$

Accepted Answer

The answer of Use a calculator to approximate the following.
(a)...

Question 17

Use a calculator to approximate $\theta$ in the interval $\left[0,90^{\circ}\right]$, if $\sin \theta=0.7313537016$.

Accepted Answer

The answer of Use a calculator to approximate $\theta$ in...

Question 18

Solve the triangle.

Accepted Answer

The answer of Solve the triangle.
 ...

Question 19

A jet leaves an airport on a bearing of $\mathrm{S} 37^{\circ} \mathrm{E}$ and travels for 324 miles. It then turns and continues on a bearing of $\mathrm{N} 53^{\circ} \mathrm{E}$ for 215 miles. How far is the jet from the airport?

Accepted Answer

The answer of A jet leaves an airport on a...

Question 20

To find the height of a fence in a baseball park, a groundskeeper found that the angle of elevation from a point 25.5 meters from the base of the fence is $23^{\circ} 54^{\prime}$. What is the height of the fence?

Accepted Answer

The answer of To find the height of a fence...

Quiz 8: The Unit Circle and Functions of Trigonometry

(a) Convert $-240^{\circ}$ to radians. (b) Convert $\frac{7 \pi}{15}$ to degrees.

A wheel is turning at a speed of 200 revolutions per minute. Through how many degrees does a point on the edge of the wheel move in 1.5 seconds?

Find the angle of smallest positive measure coterminal with $-418^{\circ}$ .

A central angle of a circle with radius 50 centimeters cuts off an arc of 120 centimeters. Find each measure. (a) The radian measure of the angle. (b) The area of the sector with this central angle.

Find the length of an arc intercepted by an angle of $60^{\circ}$ in a circle with radius 15 inches.

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=\tan (x-\pi)$

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=-\sin 4 x$

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=2 \sin \left(x+\frac{\pi}{2}\right)+1$

If $\cos \theta<0$ and $\tan \theta>0$ , in which quadrant does $\theta$ lie?

If $(-3,4)$ is on the terminal side of an angle $\theta$ in standard position, find $\sin \theta, \cos \theta$ , and $\tan \theta$ .

If $\sin \theta=\frac{3}{5}$ and $\theta$ is in quadrant II find the values of the other trigonometric functions of $\theta$ .

Find the exact values of each part labeled with a letter.

Find the exact value of $\cot \left(-480^{\circ}\right)$ .

Use a calculator to approximate the following. (a) $\cos 28^{\circ} 52^{\prime}$ (b) $\cot 52.1896^{\circ}$ (c) $\csc 19.635^{\circ}$

Use a calculator to approximate $\theta$ in the interval $\left[0,90^{\circ}\right]$ , if $\sin \theta=0.7313537016$ .

Solve the triangle.

A jet leaves an airport on a bearing of $\mathrm{S} 37^{\circ} \mathrm{E}$ and travels for 324 miles. It then turns and continues on a bearing of $\mathrm{N} 53^{\circ} \mathrm{E}$ for 215 miles. How far is the jet from the airport?

To find the height of a fence in a baseball park, a groundskeeper found that the angle of elevation from a point 25.5 meters from the base of the fence is $23^{\circ} 54^{\prime}$ . What is the height of the fence?

Quiz 8: The Unit Circle and Functions of Trigonometry

(a) Convert −240∘-240^{\circ}−240∘ to radians. (b) Convert 7π15\frac{7 \pi}{15}157π​ to degrees.

A wheel is turning at a speed of 200 revolutions per minute. Through how many degrees does a point on the edge of the wheel move in 1.5 seconds?

Find the angle of smallest positive measure coterminal with −418∘-418^{\circ}−418∘ .

A central angle of a circle with radius 50 centimeters cuts off an arc of 120 centimeters. Find each measure. (a) The radian measure of the angle. (b) The area of the sector with this central angle.

Find the length of an arc intercepted by an angle of 60∘60^{\circ}60∘ in a circle with radius 15 inches.

graph the given function over a two-period interval. Identify asymptotes when applicable. - y=tan⁡(x−π)y=\tan (x-\pi)y=tan(x−π)

graph the given function over a two-period interval. Identify asymptotes when applicable. - y=−sin⁡4xy=-\sin 4 xy=−sin4x

graph the given function over a two-period interval. Identify asymptotes when applicable. - y=2sin⁡(x+π2)+1y=2 \sin \left(x+\frac{\pi}{2}\right)+1y=2sin(x+2π​)+1

If cos⁡θ<0\cos \theta<0cosθ<0 and tan⁡θ>0\tan \theta>0tanθ>0 , in which quadrant does θ\thetaθ lie?

Use the figure to find the following: (a) The smallest positive angle coterminal with θ\thetaθ . (b) The values of xxx and yyy . (c) The values of the six trigonometric functions of θ\thetaθ . (d) The radian measure of θ\thetaθ .

If (−3,4)(-3,4)(−3,4) is on the terminal side of an angle θ\thetaθ in standard position, find sin⁡θ,cos⁡θ\sin \theta, \cos \thetasinθ,cosθ , and tan⁡θ\tan \thetatanθ .

If sin⁡θ=35\sin \theta=\frac{3}{5}sinθ=53​ and θ\thetaθ is in quadrant II find the values of the other trigonometric functions of θ\thetaθ .

Find the exact values of each part labeled with a letter.

Find the exact value of cot⁡(−480∘)\cot \left(-480^{\circ}\right)cot(−480∘) .

Use a calculator to approximate the following. (a) cos⁡28∘52′\cos 28^{\circ} 52^{\prime}cos28∘52′ (b) cot⁡52.1896∘\cot 52.1896^{\circ}cot52.1896∘ (c) csc⁡19.635∘\csc 19.635^{\circ}csc19.635∘

Use a calculator to approximate θ\thetaθ in the interval [0,90∘]\left[0,90^{\circ}\right][0,90∘] , if sin⁡θ=0.7313537016\sin \theta=0.7313537016sinθ=0.7313537016 .

Solve the triangle.

A jet leaves an airport on a bearing of S37∘E\mathrm{S} 37^{\circ} \mathrm{E}S37∘E and travels for 324 miles. It then turns and continues on a bearing of N53∘E\mathrm{N} 53^{\circ} \mathrm{E}N53∘E for 215 miles. How far is the jet from the airport?

To find the height of a fence in a baseball park, a groundskeeper found that the angle of elevation from a point 25.5 meters from the base of the fence is 23∘54′23^{\circ} 54^{\prime}23∘54′ . What is the height of the fence?

(a) Convert $-240^{\circ}$ to radians. (b) Convert $\frac{7 \pi}{15}$ to degrees.

Find the angle of smallest positive measure coterminal with $-418^{\circ}$ .

Find the length of an arc intercepted by an angle of $60^{\circ}$ in a circle with radius 15 inches.

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=\tan (x-\pi)$

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=-\sin 4 x$

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=2 \sin \left(x+\frac{\pi}{2}\right)+1$

If $\cos \theta<0$ and $\tan \theta>0$ , in which quadrant does $\theta$ lie?

If $(-3,4)$ is on the terminal side of an angle $\theta$ in standard position, find $\sin \theta, \cos \theta$ , and $\tan \theta$ .

If $\sin \theta=\frac{3}{5}$ and $\theta$ is in quadrant II find the values of the other trigonometric functions of $\theta$ .

Find the exact value of $\cot \left(-480^{\circ}\right)$ .

Use a calculator to approximate the following. (a) $\cos 28^{\circ} 52^{\prime}$ (b) $\cot 52.1896^{\circ}$ (c) $\csc 19.635^{\circ}$

Use a calculator to approximate $\theta$ in the interval $\left[0,90^{\circ}\right]$ , if $\sin \theta=0.7313537016$ .

A jet leaves an airport on a bearing of $\mathrm{S} 37^{\circ} \mathrm{E}$ and travels for 324 miles. It then turns and continues on a bearing of $\mathrm{N} 53^{\circ} \mathrm{E}$ for 215 miles. How far is the jet from the airport?

To find the height of a fence in a baseball park, a groundskeeper found that the angle of elevation from a point 25.5 meters from the base of the fence is $23^{\circ} 54^{\prime}$ . What is the height of the fence?