Question 1

the formula $s(t)=-5 \cos 3 \pi t$ 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 $s(t)=-5 \cos 3 \pi t$...

Question 2

the formula $s(t)=-5 \cos 3 \pi t$ 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 $s(t)=-5 \cos 3 \pi t$...

Question 3

(a) Convert $315^{\circ}$ to radians.
(b) Convert $\frac{11 \pi}{12}$ to degrees.

Accepted Answer

The answer of (a) Convert $315^{\circ}$ to radians.
(b) Convert \(\frac{11...

Question 4

A wheel is turning at a speed of 100 revolutions per minute. Through how many degrees does a point on the edge of the wheel move in 1.05 second?

Accepted Answer

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

Question 5

Find the angle of smallest positive measure coterminal with $-634^{\circ}$.

Accepted Answer

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

Question 6

A central angle of a circle with radius 45 centimeters cuts off an arc of 165 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 7

Find the length of an arc intercepted by an angle of $85^{\circ}$ in a circle with radius 19 inches.
graph the given function over a two-period interval. Identify asymptotes when applicable.

Accepted Answer

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

Question 8

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 9

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

Accepted Answer

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

Question 10

graph the given function over a two-period interval. Identify asymptotes when applicable
-$y=2 \cos (x+\pi)+1$

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
-The average monthly low temperature (in $\mathrm{F}^{\circ}$ ) in Paris can be modeled using the trigonometric function defined by $f(x)=12 \sin \left[\frac{\pi}{6}(x-4.1)\right]+46$, 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 Paris? 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 12

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

Accepted Answer

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

Question 13

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 14

If $(2,-6)$ 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 $(2,-6)$ is on the terminal side...

Question 15

If $\tan \theta=\frac{4}{3}$ and $\theta$ is in quadrant III find the values of the other trigonometric functions of $\theta$.

Accepted Answer

The answer of If $\tan \theta=\frac{4}{3}$ and $\theta$ is in...

Question 16

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

Accepted Answer

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

Question 17

Find the exact value of $\sec \left(585^{\circ}\right)$.

Accepted Answer

The answer of Find the exact value of $\sec \left(585^{\circ}\right)$....

Question 18

Use a calculator to approximate the following.
(a) $\tan 145^{\circ} 23^{\prime}$
(b) $\sin 38.251^{\circ}$
(c) $\sec 18.563^{\circ}$

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Solve the triangle.

Accepted Answer

The answer of Solve the triangle.
 ...

Quiz 8: The Unit Circle and Functions of Trigonometry

the formula $s(t)=-5 \cos 3 \pi t$ 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 $s(t)=-5 \cos 3 \pi t$ 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 $315^{\circ}$ to radians. (b) Convert $\frac{11 \pi}{12}$ to degrees.

A wheel is turning at a speed of 100 revolutions per minute. Through how many degrees does a point on the edge of the wheel move in 1.05 second?

Find the angle of smallest positive measure coterminal with $-634^{\circ}$ .

A central angle of a circle with radius 45 centimeters cuts off an arc of 165 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 $85^{\circ}$ in a circle with radius 19 inches. graph the given function over a two-period interval. Identify asymptotes when applicable.

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 - $y=-\cos 2 x$

graph the given function over a two-period interval. Identify asymptotes when applicable - $y=2 \cos (x+\pi)+1$

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

If $(2,-6)$ is on the terminal side of angle $\theta$ in standard position, find $\sin \theta, \cos \theta$ , and $\tan \theta$ .

If $\tan \theta=\frac{4}{3}$ 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.

Find the exact value of $\sec \left(585^{\circ}\right)$ .

Use a calculator to approximate the following. (a) $\tan 145^{\circ} 23^{\prime}$ (b) $\sin 38.251^{\circ}$ (c) $\sec 18.563^{\circ}$

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.

Quiz 8: The Unit Circle and Functions of Trigonometry

the formula s(t)=−5cos⁡3πts(t)=-5 \cos 3 \pi ts(t)=−5cos3πt 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)=−5cos⁡3πts(t)=-5 \cos 3 \pi ts(t)=−5cos3πt 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 315∘315^{\circ}315∘ to radians. (b) Convert 11π12\frac{11 \pi}{12}1211π​ to degrees.

A wheel is turning at a speed of 100 revolutions per minute. Through how many degrees does a point on the edge of the wheel move in 1.05 second?

Find the angle of smallest positive measure coterminal with −634∘-634^{\circ}−634∘ .

A central angle of a circle with radius 45 centimeters cuts off an arc of 165 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 85∘85^{\circ}85∘ in a circle with radius 19 inches. graph the given function over a two-period interval. Identify asymptotes when applicable.

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=−cos⁡2xy=-\cos 2 xy=−cos2x

graph the given function over a two-period interval. Identify asymptotes when applicable - y=2cos⁡(x+π)+1y=2 \cos (x+\pi)+1y=2cos(x+π)+1

If csc⁡θ>0\csc \theta>0cscθ>0 and sec⁡θ<0\sec \theta<0secθ<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 (2,−6)(2,-6)(2,−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 tan⁡θ=43\tan \theta=\frac{4}{3}tanθ=34​ 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.

Find the exact value of sec⁡(585∘)\sec \left(585^{\circ}\right)sec(585∘) .

Use a calculator to approximate the following. (a) tan⁡145∘23′\tan 145^{\circ} 23^{\prime}tan145∘23′ (b) sin⁡38.251∘\sin 38.251^{\circ}sin38.251∘ (c) sec⁡18.563∘\sec 18.563^{\circ}sec18.563∘

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.

the formula $s(t)=-5 \cos 3 \pi t$ 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 $s(t)=-5 \cos 3 \pi t$ 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 $315^{\circ}$ to radians. (b) Convert $\frac{11 \pi}{12}$ to degrees.

Find the angle of smallest positive measure coterminal with $-634^{\circ}$ .

Find the length of an arc intercepted by an angle of $85^{\circ}$ in a circle with radius 19 inches. graph the given function over a two-period interval. Identify asymptotes when applicable.

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 - $y=-\cos 2 x$

graph the given function over a two-period interval. Identify asymptotes when applicable - $y=2 \cos (x+\pi)+1$

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

If $(2,-6)$ is on the terminal side of angle $\theta$ in standard position, find $\sin \theta, \cos \theta$ , and $\tan \theta$ .

If $\tan \theta=\frac{4}{3}$ and $\theta$ is in quadrant III find the values of the other trigonometric functions of $\theta$ .

Find the exact value of $\sec \left(585^{\circ}\right)$ .

Use a calculator to approximate the following. (a) $\tan 145^{\circ} 23^{\prime}$ (b) $\sin 38.251^{\circ}$ (c) $\sec 18.563^{\circ}$

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