91Ó°ÊÓ

Suppose you are solving a trigonometric equation for solutions in \([0,2 \pi)\) and your work leads to $$ 2 x=\frac{2 \pi}{3}, 2 \pi, \frac{8 \pi}{3} $$ What are the corresponding values of \(x ?\)

Solve each equation for solutions over the interval \([0,2 \pi)\) by first solving for the trigonometric finction. Do not use a calculator. $$2 \cos x+1=0$$

Fill in the blank(s) to complete each fundamental identity. \(\sin ^{2} x+\cos ^{2} x=\) ________

Match each expression with the correct expression to form an identity. $$\cos (x+y)= \text {_____} $$ A. \(\cos x \cos y+\sin x \sin y\) B. \(\sin x \sin y-\cos x \cos y\) C. \(\sin x \cos y+\cos x \sin y\) D. \(\sin x \cos y-\cos x \sin y\) E. \(\cos x \sin y-\sin x \cos y\) F. \(\cos x \cos y-\sin x \sin y\)

Complete each statement, or answer the question. For a function to have an inverse, it must be ____.

Fill in the blank(s) to complete each fundamental identity. \(\tan ^{2} x+1=\) ________

Complete each statement, or answer the question. The domain of \(y=\arcsin x\) equals the ____ of \(y=\sin x\).

Solve each equation for solutions over the interval \([0,2 \pi)\) by first solving for the trigonometric finction. Do not use a calculator. $$2 \sin x+1=0$$

Match each expression with the correct expression to form an identity. $$\cos (x-y)= \text {_____} $$ A. \(\cos x \cos y+\sin x \sin y\) B. \(\sin x \sin y-\cos x \cos y\) C. \(\sin x \cos y+\cos x \sin y\) D. \(\sin x \cos y-\cos x \sin y\) E. \(\cos x \sin y-\sin x \cos y\) F. \(\cos x \cos y-\sin x \sin y\)

Suppose you are solving a trigonometric equation to find solutions in \(\left[0^{\circ}, 360^{\circ}\right)\) and your work leads to $$ \frac{1}{3} \theta=45^{\circ}, 60^{\circ}, 75^{\circ}, 90^{\circ} $$ What are the corresponding values of \(\theta ?\)