Question 1

A jet leaves an airport on a bearing of $\mathrm{N} 47^{\circ} \mathrm{W}$ and travels for 456 miles. It then turns and continues on a bearing of $\mathrm{S} 43^{\circ} \mathrm{W}$ for 381 miles. How far is the jet from the airport?

Accepted Answer

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

Question 2

To find the height of a tree, an arborist found that the angle of elevation from a point 52.6 feet from the base of the tree is $43^{\circ} 21^{\prime}$. What is the height of the tree?

Accepted Answer

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

Question 3

the formula $s(t)=-11 \cos 5 \pi t$ 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 $s(t)=-11 \cos 5 \pi t$...

Question 4

the formula $s(t)=-11 \cos 5 \pi t$ 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 $s(t)=-11 \cos 5 \pi t$...

Question 5

(a) Convert $-225^{\circ}$ to radians.
(b) Convert $\frac{3 \pi}{10}$ to degrees.

Accepted Answer

The answer of (a) Convert $-225^{\circ}$ to radians.
(b) Convert \(\frac{3...

Question 6

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 0.75 seconds?

Accepted Answer

The answer of A wheel is turning at a speed...

Question 7

Find the angle of smallest positive measure coterminal with $-828^{\circ}$.

Accepted Answer

The answer of Find the angle of smallest positive measure...

Question 8

A central angle of a circle with radius 50 centimeters cuts off an arc of 80 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 9

Find the length of an arc intercepted by an angle of $120^{\circ}$ in a circle with radius 7 inches.

Accepted Answer

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

Question 10

graph the given function over a two-period interval. Identify asymptotes when applicable.
-$y=\tan \left(x-\frac{3 \pi}{2}\right)$

Accepted Answer

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

Question 11

graph the given function over a two-period interval. Identify asymptotes when applicable.
-$y=-\sin 2 x$

Accepted Answer

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

Question 12

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 13

graph the given function over a two-period interval. Identify asymptotes when applicable.
-The average monthly high temperature $\left(\right.$ in $\mathrm{F}^{\circ}$ ) in London can be modeled using the trigonometric function defined by $f(x)=14 \sin \left[\frac{\pi}{6}(x-4.2)\right]+57$, 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 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 14

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

Accepted Answer

The answer of If $\sec \theta<0$ and $\csc \theta>0$, in...

Question 15

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 16

If $(-5,-6)$ is on the terminal side of angle $\theta$ in standard position, find $\sin \theta, \cos \theta$, and $\tan \theta$.

Accepted Answer

The answer of If $(-5,-6)$ is on the terminal side...

Question 17

If $\cos \theta=\frac{5}{13}$ and $\theta$ is in quadrant IV find the values of the other trigonometric functions of $\theta$.

Accepted Answer

The answer of If $\cos \theta=\frac{5}{13}$ and $\theta$ is in...

Question 18

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

Accepted Answer

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

Question 19

Find the exact value of $\csc \left(570^{\circ}\right)$.

Accepted Answer

The answer of Find the exact value of $\csc \left(570^{\circ}\right)$....

Question 20

Use a calculator to approximate the following.
(a) $\csc 85^{\circ} 14^{\prime}$
(b) $\cos 101.655^{\circ}$
(c) $\tan 221.125^{\circ}$

Accepted Answer

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

Quiz 8: The Unit Circle and Functions of Trigonometry

A jet leaves an airport on a bearing of $\mathrm{N} 47^{\circ} \mathrm{W}$ and travels for 456 miles. It then turns and continues on a bearing of $\mathrm{S} 43^{\circ} \mathrm{W}$ for 381 miles. How far is the jet from the airport?

To find the height of a tree, an arborist found that the angle of elevation from a point 52.6 feet from the base of the tree is $43^{\circ} 21^{\prime}$ . What is the height of the tree?

the formula $s(t)=-11 \cos 5 \pi t$ 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 $s(t)=-11 \cos 5 \pi t$ 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 $-225^{\circ}$ to radians. (b) Convert $\frac{3 \pi}{10}$ 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 0.75 seconds?

Find the angle of smallest positive measure coterminal with $-828^{\circ}$ .

A central angle of a circle with radius 50 centimeters cuts off an arc of 80 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 $120^{\circ}$ in a circle with radius 7 inches.

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=\tan \left(x-\frac{3 \pi}{2}\right)$

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=-\sin 2 x$

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

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

If $(-5,-6)$ is on the terminal side of angle $\theta$ in standard position, find $\sin \theta, \cos \theta$ , and $\tan \theta$ .

If $\cos \theta=\frac{5}{13}$ and $\theta$ is in quadrant IV 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 $\csc \left(570^{\circ}\right)$ .

Use a calculator to approximate the following. (a) $\csc 85^{\circ} 14^{\prime}$ (b) $\cos 101.655^{\circ}$ (c) $\tan 221.125^{\circ}$

Quiz 8: The Unit Circle and Functions of Trigonometry

A jet leaves an airport on a bearing of N47∘W\mathrm{N} 47^{\circ} \mathrm{W}N47∘W and travels for 456 miles. It then turns and continues on a bearing of S43∘W\mathrm{S} 43^{\circ} \mathrm{W}S43∘W for 381 miles. How far is the jet from the airport?

To find the height of a tree, an arborist found that the angle of elevation from a point 52.6 feet from the base of the tree is 43∘21′43^{\circ} 21^{\prime}43∘21′ . What is the height of the tree?

the formula s(t)=−11cos⁡5πts(t)=-11 \cos 5 \pi ts(t)=−11cos5πt 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)=−11cos⁡5πts(t)=-11 \cos 5 \pi ts(t)=−11cos5πt 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 −225∘-225^{\circ}−225∘ to radians. (b) Convert 3π10\frac{3 \pi}{10}103π​ 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 0.75 seconds?

Find the angle of smallest positive measure coterminal with −828∘-828^{\circ}−828∘ .

A central angle of a circle with radius 50 centimeters cuts off an arc of 80 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 120∘120^{\circ}120∘ in a circle with radius 7 inches.

graph the given function over a two-period interval. Identify asymptotes when applicable. - y=tan⁡(x−3π2)y=\tan \left(x-\frac{3 \pi}{2}\right)y=tan(x−23π​)

graph the given function over a two-period interval. Identify asymptotes when applicable. - y=−sin⁡2xy=-\sin 2 xy=−sin2x

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 sec⁡θ<0\sec \theta<0secθ<0 and csc⁡θ>0\csc \theta>0cscθ>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 (−5,−6)(-5,-6)(−5,−6) is on the terminal side of angle θ\thetaθ in standard position, find sin⁡θ,cos⁡θ\sin \theta, \cos \thetasinθ,cosθ , and tan⁡θ\tan \thetatanθ .

If cos⁡θ=513\cos \theta=\frac{5}{13}cosθ=135​ and θ\thetaθ is in quadrant IV 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 csc⁡(570∘)\csc \left(570^{\circ}\right)csc(570∘) .

Use a calculator to approximate the following. (a) csc⁡85∘14′\csc 85^{\circ} 14^{\prime}csc85∘14′ (b) cos⁡101.655∘\cos 101.655^{\circ}cos101.655∘ (c) tan⁡221.125∘\tan 221.125^{\circ}tan221.125∘

A jet leaves an airport on a bearing of $\mathrm{N} 47^{\circ} \mathrm{W}$ and travels for 456 miles. It then turns and continues on a bearing of $\mathrm{S} 43^{\circ} \mathrm{W}$ for 381 miles. How far is the jet from the airport?

To find the height of a tree, an arborist found that the angle of elevation from a point 52.6 feet from the base of the tree is $43^{\circ} 21^{\prime}$ . What is the height of the tree?

the formula $s(t)=-11 \cos 5 \pi t$ 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 $s(t)=-11 \cos 5 \pi t$ 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 $-225^{\circ}$ to radians. (b) Convert $\frac{3 \pi}{10}$ to degrees.

Find the angle of smallest positive measure coterminal with $-828^{\circ}$ .

Find the length of an arc intercepted by an angle of $120^{\circ}$ in a circle with radius 7 inches.

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=\tan \left(x-\frac{3 \pi}{2}\right)$

graph the given function over a two-period interval. Identify asymptotes when applicable. - $y=-\sin 2 x$

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

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

If $(-5,-6)$ is on the terminal side of angle $\theta$ in standard position, find $\sin \theta, \cos \theta$ , and $\tan \theta$ .

If $\cos \theta=\frac{5}{13}$ and $\theta$ is in quadrant IV find the values of the other trigonometric functions of $\theta$ .

Find the exact value of $\csc \left(570^{\circ}\right)$ .

Use a calculator to approximate the following. (a) $\csc 85^{\circ} 14^{\prime}$ (b) $\cos 101.655^{\circ}$ (c) $\tan 221.125^{\circ}$