91Ó°ÊÓ

When solving a trigonometric equation, the preliminary goal is to ________ the trigonometric function involved in the equation.

The equation \( 2 \sin \theta + 1 = 0 \) has the solutions \( \theta = \frac{7\pi}{6} + 2n\pi \) and \( \theta = \frac{11\pi}{6} + 2n\pi \), which are called ________ solutions.

In Exercises 5-10, verify that the \( x \)-values are solutions of the equation. \( \csc^4 x - 4 \csc^2 x = 0 \) (a) \( x = \dfrac{\pi}{6} \) (b) \( x = \dfrac{5\pi}{6} \)

In Exercises 9-50, verify the identity \( \cos x + \sin x \tan x = \sec x \)

In Exercises 25 - 30, match the trigonometric expression with one of the following. (a)\( \sec x \) (b) \( -1 \) (c) \( \cot x \) (d) \( 1 \) (e) \( -\tan x \) (d) \( \sin x \) \( \sec x \cos x \)

In Exercises 25 - 30, match the trigonometric expression with one of the following. (a)\( \sec x \) (b) \( -1 \) (c) \( \cot x \) (d) \( 1 \) (e) \( -\tan x \) (d) \( \sin x \) \( \dfrac{\sin(-x)}{\cos(-x)} \)

In Exercises 25-38, find all solutions of the equation in the interval \( [0, 2\pi) \). \( \sin x - 2 = \cos x - 2 \)

Exercises 43-52, use the power-reducing formulas to rewrite the expression in terms of the first power of the cosine. \( \cos^4 x \)

Exercises 43-52, use the power-reducing formulas to rewrite the expression in terms of the first power of the cosine. \( \cos^4 2x \)

Exercises 43-52, use the power-reducing formulas to rewrite the expression in terms of the first power of the cosine. \( \sin^2 x \cos^4 x \)