91Ó°ÊÓ

Use the half-angle identities to find the exact values of the trigonometric expressions. $$\sec \left(\frac{5 \pi}{8}\right)$$

Refer to the following: Sum and difference identities can be used to simplify more complicated expressions. For instance, the sine and cosine function can be represented by infinite polynomials called power series. $$ \begin{aligned} \cos x &=1-\frac{x^{2}}{2 !}+\frac{x^{4}}{4 !}-\frac{x^{6}}{6 !}+\frac{x^{8}}{8 !}-\cdots \\ \sin x &=x-\frac{x^{3}}{3 !}+\frac{x^{5}}{5 !}-\frac{x^{7}}{7 !}+\frac{x^{9}}{9 !}-\cdots \end{aligned} $$ Power Series. Find the power series that represents \(\sin \left(x+\frac{3 \pi}{2}\right)\)

Solve the trigonometric equations exactly on the indicated interval, \(0 \leq x<2 \pi\). $$\sin x+\csc x=2$$

$$\text { Graph } y=x-\cos (2 x) \sin (3 x)$$

Evaluate each expression exactly, if possible. If not possible, state why. $$\sec \left[\sec ^{-1}\left(\frac{1}{2}\right)\right]$$

Use the half-angle identities to find the exact values of the trigonometric expressions. $$\csc \left(-\frac{5 \pi}{8}\right)$$

Verify each of the trigonometric identities. $$\tan x(\csc x-\sin x)=\cos x$$

Determine whether each equation is a conditional equation or an identity. $$\cos ^{2} x(\tan x-\sec x)(\tan x+\sec x)=1$$

Evaluate each expression exactly, if possible. If not possible, state why. $$\csc \left[\csc ^{-1}\left(\frac{1}{2}\right)\right]$$

Solve the trigonometric equations exactly on the indicated interval, \(0 \leq x<2 \pi\). $$\sec x-\tan x=\frac{\sqrt{3}}{3}$$