Question 1

Use a calculator to approximate $\theta$ to the nearest tenth in the interval $\left[0,90^{\circ}\right]$, if $\cos \theta=0.9086146585$.

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Question 2

Solve the triangle.

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 ...

Question 3

A jet leaves an airport on a bearing of $\mathrm{S} 29^{\circ} \mathrm{W}$ and travels for 245 miles. It then turns and continues on a bearing of $\mathrm{N} 61^{\circ} \mathrm{W}$ for 506 miles. How far is the jet from the airport?

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Question 4

To find the height of a building, a surveyor found that the angle of elevation from a point 42.5 feet from the base of the building is $79^{\circ} 15^{\prime}$. What is the height of the building?

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The answer of To find the height of a building,...

Question 5

the formula $s(t)=-9 \cos \frac{\pi}{2} t$ gives the height (in inches) of a weight attached to a spring after $t$ seconds.
-Find the maximum height that the weight rises above the equilibrium position of $y=0$.

Accepted Answer

The answer of the formula $s(t)=-9 \cos \frac{\pi}{2} t$ gives...

Question 6

the formula $s(t)=-9 \cos \frac{\pi}{2} t$ gives the height (in inches) of a weight attached to a spring after $t$ seconds.
-When does the weight reach its maximum height if $t \geq 0$ ?

Accepted Answer

The answer of the formula $s(t)=-9 \cos \frac{\pi}{2} t$ gives...

Question 7

(a) Convert $300^{\circ}$ to radians.
(b) Convert $-\frac{11 \pi}{30}$ to degrees.

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(b) Convert \(-\frac{11...

Question 8

A wheel is turning at a speed of 72 revolutions per minute. Through how many degrees does a point on the edge of the wheel move in 3 seconds?

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Question 9

Find the angle of smallest positive measure coterminal with $-559^{\circ}$.

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Question 10

A central angle of a circle with radius 35 centimeters cuts off an arc of 100 centimeters. Find each measure.
(a) The radian measure of the angle.
(b) The area of the sector with this central angle.

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Question 11

Find the length of an arc intercepted by an angle of $235^{\circ}$ in a circle with radius 27 inches.

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Question 12

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

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Question 13

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

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Question 14

graph the given function over a two-period interval. Identify asymptotes when applicable.
-$y=3 \cos (x-\pi)+2$

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Question 15

graph the given function over a two-period interval. Identify asymptotes when applicable.
-The average monthly high temperature (in $\mathrm{F}^{\circ}$ ) in Paris can be modeled using the trigonometric function defined by $f(x)=16.5 \sin \left[\frac{\pi}{6}(x-4.1)\right]+59.5$, 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 high temperature for the month of October?
(d) Find the maximum and minimum average monthly high temperatures and the months when they occur.
(e) What would be an approximation for the average yearly high temperature in Paris? How is this related to the vertical translation of the sine function in the formula for $f$ ?

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Question 16

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

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Question 17

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 $\theta$.

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...

Question 18

If $(-3,-5)$ is on the terminal side of an angle $\theta$ in standard position, find $\sin \theta, \cos \theta$, and $\tan \theta$.

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Question 19

If $\cos \theta=-\frac{7}{25}$ and $\theta$ is in quadrant III find the values of the other trigonometric functions of $\theta$.

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Question 20

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

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Quiz 8: The Unit Circle and Functions of Trigonometry

Use a calculator to approximate $\theta$ to the nearest tenth in the interval $\left[0,90^{\circ}\right]$ , if $\cos \theta=0.9086146585$ .

Solve the triangle.

A jet leaves an airport on a bearing of $\mathrm{S} 29^{\circ} \mathrm{W}$ and travels for 245 miles. It then turns and continues on a bearing of $\mathrm{N} 61^{\circ} \mathrm{W}$ for 506 miles. How far is the jet from the airport?

To find the height of a building, a surveyor found that the angle of elevation from a point 42.5 feet from the base of the building is $79^{\circ} 15^{\prime}$ . What is the height of the building?

the formula $s(t)=-9 \cos \frac{\pi}{2} t$ gives the height (in inches) of a weight attached to a spring after $t$ seconds. -Find the maximum height that the weight rises above the equilibrium position of $y=0$ .

the formula $s(t)=-9 \cos \frac{\pi}{2} t$ gives the height (in inches) of a weight attached to a spring after $t$ seconds. -When does the weight reach its maximum height if $t \geq 0$ ?

(a) Convert $300^{\circ}$ to radians. (b) Convert $-\frac{11 \pi}{30}$ to degrees.

A wheel is turning at a speed of 72 revolutions per minute. Through how many degrees does a point on the edge of the wheel move in 3 seconds?

Find the angle of smallest positive measure coterminal with $-559^{\circ}$ .

A central angle of a circle with radius 35 centimeters cuts off an arc of 100 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 $235^{\circ}$ in a circle with radius 27 inches.

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

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

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=3 \cos (x-\pi)+2$

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

If $(-3,-5)$ is on the terminal side of an angle $\theta$ in standard position, find $\sin \theta, \cos \theta$ , and $\tan \theta$ .

If $\cos \theta=-\frac{7}{25}$ and $\theta$ is in quadrant III find the values of the other trigonometric functions of $\theta$ .

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

Quiz 8: The Unit Circle and Functions of Trigonometry

Use a calculator to approximate θ\thetaθ to the nearest tenth in the interval [0,90∘]\left[0,90^{\circ}\right][0,90∘] , if cos⁡θ=0.9086146585\cos \theta=0.9086146585cosθ=0.9086146585 .

Solve the triangle.

A jet leaves an airport on a bearing of S29∘W\mathrm{S} 29^{\circ} \mathrm{W}S29∘W and travels for 245 miles. It then turns and continues on a bearing of N61∘W\mathrm{N} 61^{\circ} \mathrm{W}N61∘W for 506 miles. How far is the jet from the airport?

To find the height of a building, a surveyor found that the angle of elevation from a point 42.5 feet from the base of the building is 79∘15′79^{\circ} 15^{\prime}79∘15′ . What is the height of the building?

the formula s(t)=−9cos⁡π2ts(t)=-9 \cos \frac{\pi}{2} ts(t)=−9cos2π​t gives the height (in inches) of a weight attached to a spring after ttt seconds. -Find the maximum height that the weight rises above the equilibrium position of y=0y=0y=0 .

the formula s(t)=−9cos⁡π2ts(t)=-9 \cos \frac{\pi}{2} ts(t)=−9cos2π​t gives the height (in inches) of a weight attached to a spring after ttt seconds. -When does the weight reach its maximum height if t≥0t \geq 0t≥0 ?

(a) Convert 300∘300^{\circ}300∘ to radians. (b) Convert −11π30-\frac{11 \pi}{30}−3011π​ to degrees.

A wheel is turning at a speed of 72 revolutions per minute. Through how many degrees does a point on the edge of the wheel move in 3 seconds?

Find the angle of smallest positive measure coterminal with −559∘-559^{\circ}−559∘ .

A central angle of a circle with radius 35 centimeters cuts off an arc of 100 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 235∘235^{\circ}235∘ in a circle with radius 27 inches.

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

graph the given function over a two-period interval. Identify asymptotes when applicable. - y=−cos⁡4xy=-\cos 4 xy=−cos4x

graph the given function over a two-period interval. Identify asymptotes when applicable. - y=3cos⁡(x−π)+2y=3 \cos (x-\pi)+2y=3cos(x−π)+2

If csc⁡θ<0\csc \theta<0cscθ<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,−5)(-3,-5)(−3,−5) 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 cos⁡θ=−725\cos \theta=-\frac{7}{25}cosθ=−257​ and θ\thetaθ is in quadrant III find the values of the other trigonometric functions of θ\thetaθ .

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

Use a calculator to approximate $\theta$ to the nearest tenth in the interval $\left[0,90^{\circ}\right]$ , if $\cos \theta=0.9086146585$ .

A jet leaves an airport on a bearing of $\mathrm{S} 29^{\circ} \mathrm{W}$ and travels for 245 miles. It then turns and continues on a bearing of $\mathrm{N} 61^{\circ} \mathrm{W}$ for 506 miles. How far is the jet from the airport?

To find the height of a building, a surveyor found that the angle of elevation from a point 42.5 feet from the base of the building is $79^{\circ} 15^{\prime}$ . What is the height of the building?

the formula $s(t)=-9 \cos \frac{\pi}{2} t$ gives the height (in inches) of a weight attached to a spring after $t$ seconds. -Find the maximum height that the weight rises above the equilibrium position of $y=0$ .

the formula $s(t)=-9 \cos \frac{\pi}{2} t$ gives the height (in inches) of a weight attached to a spring after $t$ seconds. -When does the weight reach its maximum height if $t \geq 0$ ?

(a) Convert $300^{\circ}$ to radians. (b) Convert $-\frac{11 \pi}{30}$ to degrees.

Find the angle of smallest positive measure coterminal with $-559^{\circ}$ .

Find the length of an arc intercepted by an angle of $235^{\circ}$ in a circle with radius 27 inches.

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

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

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=3 \cos (x-\pi)+2$

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

If $(-3,-5)$ is on the terminal side of an angle $\theta$ in standard position, find $\sin \theta, \cos \theta$ , and $\tan \theta$ .

If $\cos \theta=-\frac{7}{25}$ and $\theta$ is in quadrant III find the values of the other trigonometric functions of $\theta$ .