91Ó°ÊÓ

Use a calculator to evaluate \(\sec \theta, \csc \theta,\) and cot \(\theta\) for the given value of \(\theta .\) Round the answers to two decimal places. $$-6 \pi / 5$$

Suppose that $$A \sin \theta+\cos \theta=1 \quad \text { and } \quad B \sin \theta-\cos \theta=1$$ Show that \(A B=1 .\) Hint: Solve the first equation for \(A\) the second for \(B\), and then compute \(A B\).

If \(\sin \alpha+\cos \alpha=a\) and \(\sin \alpha-\cos \alpha=b,\) show that $$\tan \alpha=\frac{a+b}{a-b}$$

If \(a \sin ^{2} \theta+b \cos ^{2} \theta=1,\) show that $$\sin ^{2} \theta=\frac{1-b}{a-b} \quad \text { and } \quad \tan ^{2} \theta=\frac{b-1}{1-a}$$

Use a calculator to evaluate \(\sec \theta, \csc \theta,\) and cot \(\theta\) for the given value of \(\theta .\) Round the answers to two decimal places. $$1400+2 \pi$$

Use a calculator to evaluate \(\sec \theta, \csc \theta,\) and cot \(\theta\) for the given value of \(\theta .\) Round the answers to two decimal places. $$33^{\circ}$$

(a) Choose (at random) an angle \(\theta\) such that \(0^{\circ}<\theta<90^{\circ} .\) Then with this value of \(\theta,\) use your calculator to verify that \(\log _{10}\left(\sin ^{2} \theta\right)=2 \log _{10}(\sin \theta)\) (b) For which values of \(\theta\) in the interval \(0^{\circ} \leq \theta \leq 180^{\circ}\) is the equation in part (a) valid?

Use a calculator to evaluate \(\sec \theta, \csc \theta,\) and cot \(\theta\) for the given value of \(\theta .\) Round the answers to two decimal places. $$393^{\circ}$$

(a) Choose (at random) an angle \(\theta\) such that \(0^{\circ}<\theta<90^{\circ} .\) Then with this value of \(\theta,\) use your calculator to verify that \(\log _{10}\left(\cos ^{2} \theta\right)=2 \log _{10}(\cos \theta)\) (b) For which values of \(\theta\) in the interval \(0^{\circ} \leq \theta \leq 180^{\circ}\) is the equation in part (a) valid?

Use a calculator to evaluate \(\sec \theta, \csc \theta,\) and cot \(\theta\) for the given value of \(\theta .\) Round the answers to two decimal places. $$-125^{\circ}$$