91Ó°ÊÓ

Six functions are defined as follows: $$\begin{aligned}&f(x)=\sin x \quad g(x)=\csc x \quad h(x)=\pi x-\frac{\pi}{6}\\\&F(x)=\cos x \quad G(x)=\sec x \quad H(x)=\pi x+\frac{\pi}{4}\end{aligned}$$ In each case, graph the indicated function for one period. (a) \(F \circ h\) (b) \(G \circ h\)

Use the Pythagorean identities to simplify the given expressions. $$\frac{\csc ^{4} \theta-\cot ^{4} \theta}{\csc ^{2} \theta+\cot ^{2} \theta}$$

Prove that the equations are identities. $$\csc t=\sin t+\cot t \cos t$$

Four functions are defined as follows: Four functions are defined as follows: $$\begin{array}{ll}f(x)=\csc x & T(x)=\tan x \\\g(x)=\sec x & A(x)=|x|\end{array}$$ In each case, graph the indicated function over the interval \([-2 \pi, 2 \pi]\). $$A \circ T$$

Four functions are defined as follows: $$\begin{array}{ll}f(x)=\csc x & T(x)=\tan x \\\g(x)=\sec x & A(x)=|x|\end{array}$$ In each case, graph the indicated function over the interval \([-2 \pi, 2 \pi]\). $$A \circ g$$

Prove that the equations are identities. $$\sin ^{2} t-\cos ^{2} t=\frac{1-\cot ^{2} t}{1+\cot ^{2} t}$$

Four functions are defined as follows: $$\begin{array}{ll}f(x)=\csc x & T(x)=\tan x \\\g(x)=\sec x & A(x)=|x|\end{array}$$ In each case, graph the indicated function over the interval \([-2 \pi, 2 \pi]\). $$A \circ f$$

Prove that the equations are identities. $$\frac{1}{1+\sec s}+\frac{1}{1-\sec s}=-2 \cot ^{2} s$$

Prove that the equations are identities. $$\frac{1+\tan s}{1-\tan s}=\frac{\sec ^{2} s+2 \tan s}{2-\sec ^{2} s}$$

Four functions are defined as follows: $$\begin{array}{ll}f(x)=\csc x & T(x)=\tan x \\\g(x)=\sec x & A(x)=|x|\end{array}$$ In each case, graph the indicated function over the interval \([-2 \pi, 2 \pi]\). $$f \circ A$$