91Ó°ÊÓ

Find all solutions of the equation. $$\cos t=-1$$

Use sum-to-product formulas to find the solutions of the equation. $$\cos 3 x+\cos 5 x=\cos x$$

Graphically solve the trigonometric equation on the indicated interval to two decimal places. $$2 \cot \frac{1}{4} x=1-\sec \frac{1}{2} x ; \quad[-2 \pi, 2 \pi]$$

The average monthly high temperature \(T\) (in "F) in Augusta, Georgia, can be approximated using the function $$ T(t)=17 \cos \left(\frac{\pi}{6} t-\frac{7 \pi}{6}\right)+75 $$ where \(t\) is in months and \(t=1\) corresponds to January. (a) Graph \(T\) over the two-year interval \([1,25]\) (b) Calculate the average high temperature in April and in December. (c) Graphically approximate the months when the average high temperature is \(67^{\circ} \mathrm{F}\) or lower.

Many calculators have viewing screens that are wider than they are high. The approximate ratio of the height to the width is often \(2: 3 .\) Let the actual height of the calculator screen along the \(y\) -axis be 2 units, the actual width of the calculator screen along the \(x\) -axis be 3 units, and Xscl \(=\mathbf{Y s c l}=1 .\) since the line \(y=x\) must pass through the point \((1,1),\) the actual slope \(m_{\mathrm{A}}\) of this line on the calcuIator screen is given by \(m_{\mathrm{A}}=\frac{\text { actual distance between tick marks on } y \text { zaxis }}{\text { actual distance between tick marks on } x \text { -axis }}\) Using this information, graph \(y=x\) in the given viewing rectangle and predict the actual angle \(\boldsymbol{\theta}\) that the graph makes with the \(x\) -axis on the viewing screen. $$[0,3] \text { by }[0,2]$$