91Ó°ÊÓ

True or False The graph of the sine function has infinitely many \(x\) -intercepts.

Find the amplitude (if one exists), period, and phase shift of each function. Graph each function. Be sure to label key points. Show at least two periods. $$ y=2 \cos (2 \pi x+4)+4 $$

Draw each angle in standard position. \(-120^{\circ}\)

A point on the terminal side of an angle \(\theta\) in standard position is given. Find the exact value of each of the six trigonometric functions of \(\theta .\) $$ \left(\frac{\sqrt{3}}{2}, \frac{1}{2}\right) $$

Determine the amplitude and period of each function without graphing. $$ y=6 \sin (\pi x) $$

A point on the terminal side of an angle \(\theta\) in standard position is given. Find the exact value of each of the six trigonometric functions of \(\theta .\) $$ \left(\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right) $$

A point on the terminal side of an angle \(\theta\) in standard position is given. Find the exact value of each of the six trigonometric functions of \(\theta .\) $$ \left(-\frac{\sqrt{2}}{2},-\frac{\sqrt{2}}{2}\right) $$

Use a coterminal angle to find the exact value of each expression. Do not use a calculator. $$ \cos 420^{\circ} $$

Use a coterminal angle to find the exact value of each expression. Do not use a calculator. $$ \sin 390^{\circ} $$

The data on the next page represent the average monthly temperatures for Washington, D.C. (a) Draw a scatter plot of the data for one period. (b) Find a sinusoidal function of the form \(y=A \sin (\omega x-\phi)+B\) that models the data. $$ \begin{array}{|lc|} \hline \text { Decade, } x & \text { Major Hurricanes, } \boldsymbol{H} \\ \hline 1921-1930,1 & 17 \\ 1931-1940,2 & 16 \\ 1941-1950,3 & 29 \\ 1951-1960,4 & 33 \\ 1961-1970,5 & 27 \\ 1971-1980,6 & 16 \\ 1981-1990,7 & 16 \\ 1991-2000,8 & 27 \\ 2001-2010,9 & 33 \\ \hline \end{array} $$ (c) Draw the sinusoidal function found in part (b) on the scatter plot. (d) Use a graphing utility to find the sinusoidal function of best fit. (e) Graph the sinusoidal function of best fit on a scatter plot of the data. $$ \begin{array}{lc|} \hline \text { Month, } \boldsymbol{x} & \begin{array}{c} \text { Average Monthly } \\ \text { Temperature, }^{\circ} \mathrm{F} \end{array} \\ \hline \text { January, } 1 & 36.0 \\ \text { February, } 2 & 39.0 \\ \text { March, } 3 & 46.8 \\ \text { April, } 4 & 56.8 \\ \text { May, } 5 & 66.0 \\ \text { June, } 6 & 75.2 \\ \text { July, } 7 & 79.8 \\ \text { August, } 8 & 78.1 \\ \text { September, } 9 & 71.0 \\ \text { October, } 10 & 59.5 \\ \text { November, } 11 & 49.6 \\ \text { December, } 12 & 39.7 \end{array} $$