use a graphing utility to graph the function. Include two full periods. Be sure to choose an appropriate viewing window.

$$y=\frac{1}{100}\sin120\pi t$$

graph the functions $f$ and $g.$ Use the graphs to make a conjecture about the relationship between the functions.

$$f(x)=\sin x+\cos(x+\frac{\pi}{2}),g(x)=0$$

write an algebraic expression that is equivalent to the expression. $(Hint$: Sketch a right triangle, as demonstrated in Example $7.)\newline$

$$\sec[\arcsin(x-1)]$$

find the values of the remaining five trigonometric functions of $\theta\newline$

$$\underline{Function\space Value}\qquad\underline{Constraints}\newline\cos\theta=-\frac{2}{5}\qquad\qquad\quad\sin\theta>0$$

A student you are tutoring has used a unit circle divided into $8$ equal parts to complete the table for selected values of $t$. What is wrong?

The table shows the average sales $S$ (in millions of dollars) of an outerwear manufacturer for each month $t,$ where $t=1$ represents January.

$\newline$Interpret the meaning of the model’s amplitude in the context of the problem.

Graphical Analysis With your graphing utility in radian and parametric modes, enter the equations $X_{1 \mathrm{~T}}=\cos \mathrm{T}$ and $Y_{\mathrm{IT}}=\sin \mathrm{T}$ and use the following settings.

$$\mathrm{T min} =0, \mathrm{T \max} =6.3, \mathrm{Tstep} =0.1$$

$$\mathrm{X min} =-1.5, \mathrm{Xmax}=1.5, \mathrm{Xscl}=1$$

$$\mathrm{Y min} =-1, \mathrm{Ymax}=1, \mathrm{Yscl}=1$$

Graph the entered equations and describe the graph.

The table shows the average sales $S$ (in millions of dollars) of an outerwear manufacturer for each month $t,$ where $t=1$ represents January.

$\newline$What is the period of the model$?$Do you think it is reasonable given the context$?$ Explain your reasoning.

for the simple harmonic motion described by the trigonometric function, find the least positive value of $t$ for which $d=0$. Use a graphing utility to verify your results.

$$d=\frac{1}{2} \cos 20 \pi t$$

The table shows the average sales $S$ (in millions of dollars) of an outerwear manufacturer for each month $t,$ where $t=1$ represents January.

$\newline$Find a trigonometric model that fits the data. Graph the model on your scatter plot. How well does the model fit the data$?$

for the simple harmonic motion described by the trigonometric function, find the frequency.

$$d=\frac{1}{2} \cos 20 \pi t$$

use a graphing utility to graph the function. Include two full periods. Be sure to choose an appropriate viewing window.

$$y=-0.1\sin(\frac{\pi x}{10}+\pi)$$

The table shows the average sales $S$ (in millions of dollars) of an outerwear manufacturer for each month $t,$ where $t=1$ represents January.

$\newline$Create a scatter plot of the data.

for the simple harmonic motion described by the trigonometric function, find the maximum displacement.

$$d=\frac{1}{2} \cos 20 \pi t$$