6.1 Graphs of the sine and cosine functions  (Page 8/13)

For the equation $A\cos (Bx+C)+D,$ what constants affect the range of the function and how do they affect the range?

How does the range of a translated sine function relate to the equation $y=A\sin (Bx+C)+D?$

How can the unit circle be used to construct the graph of $f(t)=\sin t?$

$f(x)=2\sin x$

$f(x)=\frac{2}{3}\cos x$

$f(x)=-3\sin x$

$f(x)=4\sin x$

$f(x)=2\cos x$

$f\left(x\right)=\cos \left(2x\right)$

$f(x)=2\sin \left(\frac{1}{2}x\right)$

$f(x)=4\cos (\pi x)$

$f(x)=3\cos \left(\frac{6}{5}x\right)$

$y=3\sin (8(x+4))+5$

$y=2\sin (3x-21)+4$

$y=5\sin (5x+20)-2$

$f\left(t\right)=2\sin \left(t-\frac{5\pi }{6}\right)$

$f(t)=-\cos \left(t+\frac{\pi }{3}\right)+1$

$f\left(t\right)=4\cos \left(2\left(t+\frac{\pi }{4}\right)\right)-3$

$f\left(t\right)=-\sin \left(\frac{1}{2}t+\frac{5\pi }{3}\right)$

$f\left(x\right)=4\sin \left(\frac{\pi }{2}\left(x-3\right)\right)+7$

Determine the amplitude, midline, period, and an equation involving the sine function for the graph shown in [link] .

Determine the amplitude, period, midline, and an equation involving cosine for the graph shown in [link] .

Determine the amplitude, period, midline, and an equation involving cosine for the graph shown in [link] .

Determine the amplitude, period, midline, and an equation involving sine for the graph shown in [link] .

Determine the amplitude, period, midline, and an equation involving cosine for the graph shown in [link] .

Determine the amplitude, period, midline, and an equation involving sine for the graph shown in [link] .

Determine the amplitude, period, midline, and an equation involving cosine for the graph shown in [link] .

Determine the amplitude, period, midline, and an equation involving sine for the graph shown in [link] .

On $[0,2\pi ),$ solve $f\left(x\right)=0.$

On $[0,2\pi ),$ solve $f\left(x\right)=\frac{1}{2}.$

Evaluate $f\left(\frac{\pi }{2}\right).$

On $[0,2\pi ),f(x)=\frac{\sqrt{2}}{2}.$ Find all values of $x.$

On $[0,2\pi ),$ the maximum value(s) of the function occur(s) at what x -value(s)?

On $[0,2\pi ),$ the minimum value(s) of the function occur(s) at what x -value(s)?

Show that $f(-x)=-f(x).$ This means that $f(x)=\sin x$ is an odd function and possesses symmetry with respect to ________________.

On $[0,2\pi ),$ solve the equation $f(x)=\cos x=0.$

On $[0,2\pi ),$ solve $f(x)=\frac{1}{2}.$

On $[0,2\pi ),$ find the x -intercepts of $f(x)=\cos x.$

On $[0,2\pi ),$ find the x -values at which the function has a maximum or minimum value.

On $[0,2\pi ),$ solve the equation $f(x)=\frac{\sqrt{3}}{2}.$

Graph $h(x)=x+\sin x$ on $\left[0,2\pi \right].$ Explain why the graph appears as it does.

Graph $h(x)=x+\sin x$ on $\left[-100,100\right].$ Did the graph appear as predicted in the previous exercise?

Graph $f(x)=x\sin x$ on $\left[0,2\pi \right]$ and verbalize how the graph varies from the graph of $f(x)=\sin x.$

Graph $f(x)=x\sin x$ on the window $\left[\mathrm{-10},10\right]$ and explain what the graph shows.

Graph $f(x)=\frac{\sin x}{x}$ on the window $\left[\mathrm{-5}\pi ,5\pi \right]$ and explain what the graph shows.

A Ferris wheel is 25 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. The function $h\left(t\right)$ gives a person’s height in meters above the ground t minutes after the wheel begins to turn.

1. Find the amplitude, midline, and period of $h\left(t\right).$
2. Find a formula for the height function $h\left(t\right).$
3. How high off the ground is a person after 5 minutes?