91Ó°ÊÓ

Write each expression as a product of trigonometric functions. $$\cos 4 x-\cos 2 x$$

Match each expression in Column I with its value in Column II. $$\mathbf{I}$$ $$\sin \left(-105^{\circ}\right)$$ $$\mathbf{II}$$ A. \(\frac{\sqrt{6}+\sqrt{2}}{4}\) B. \(\frac{-\sqrt{6}-\sqrt{2}}{4}\) C. \(\frac{\sqrt{6}-\sqrt{2}}{4}\) D. \(2+\sqrt{3}\) E. \(2-\sqrt{3}\) F. \(-2-\sqrt{3}\)

Verify that each trigonometric equation is an identity. $$(\sec \alpha-\tan \alpha)^{2}=\frac{1-\sin \alpha}{1+\sin \alpha}$$

Alternating Electric Current In the study of alternating electric current, instantaneous voltage is modeled by $$E=E_{\max } \sin 2 \pi f t$$ where \(f\) is the number of cycles per second, \(E_{\max }\) is the maximum voltage, and \(t\) is time in seconds. (a) Solve the equation for \(t\) (b) Find the least positive value of \(t\) if \(E_{\max }=12, E=5,\) and \(f=100 .\) Use a calculator.

Verify that each trigonometric equation is an identity. $$\frac{\sec ^{4} \theta-\tan ^{4} \theta}{\sec ^{2} \theta+\tan ^{2} \theta}=\sec ^{2} \theta-\tan ^{2} \theta$$

Verify that each trigonometric equation is an identity. $$\frac{\tan ^{2} t-1}{\sec ^{2} t}=\frac{\tan t-\cot t}{\tan t+\cot t}$$

Write each expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression and all functions are of \(\theta\) only. $$(\sec \theta+\csc \theta)(\cos \theta-\sin \theta)$$

Explain why attempting to find \(\sin ^{-1} 1.003\) on your calculator will result in an error message.

Write each expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression and all functions are of \(\theta\) only. $$\sin \theta(\csc \theta-\sin \theta)$$

Solve each equation ( \(x\) in radians and \(\theta\) in degrees) for all exact solutions where appropriate. Round approximate answers in radians to four decimal places and approximate answers in degrees to the nearest tenth. Write answers using the least possible nonnegative angle measures. $$2 \sqrt{3} \cos \frac{x}{2}=-3$$