CHAPTER 20 PRACTICE TEST

As a study aid, we have included complete solutions for each Practice Test problem at the end of this book.

Prove that $\sec θ - \frac{\tan θ}{\csc θ} = \cos θ .$ $\sec θ - \frac{\tan θ}{\csc θ} = \cos θ .$
Solve for $x (0 \leq x < 2 π)$ $x (0 \leq x < 2 π)$ analytically, using trigonometric relations where necessary: $\sin 2 x + \sin x = 0 .$ $\sin 2 x + \sin x = 0 .$
Find an algebraic expression for $\cos (\sin^{- 1} x) .$ $\cos (\sin^{- 1} x) .$
The electric current as a function of the time for a particular circuit is given by $i = 8.00 e^{- 20 t} (1.73 \cos 10.0 t - \sin 10.0 t) .$ $i = 8.00 e^{- 20 t} (1.73 \cos 10.0 t - \sin 10.0 t) .$ Find the time (in s) when the current is first zero.
Prove that $\frac{\tan α + \tan β}{\tan α - \tan β} = \frac{\sin (α + β)}{\sin (α - β)} .$ $\frac{\tan α + \tan β}{\tan α - \tan β} = \frac{\sin (α + β)}{\sin (α - β)} .$
Prove that $\cot^{2} x - \cos^{2} x = \cot^{2} {x \cos}^{2} x .$ $\cot^{2} x - \cos^{2} x = \cot^{2} {x \cos}^{2} x .$
Find $\cos \frac{1}{2} x$ $\cos \frac{1}{2} x$ if $\sin x = - \frac{3}{5}$ $\sin x = - \frac{3}{5}$ and $270 ° < x < 360 ° .$ $270 ° < x < 360 ° .$
The intensity of a certain type of polarized light is given by $I = I_{0} \sin 2 θ \cos 2 θ .$ $I = I_{0} \sin 2 θ \cos 2 θ .$ Solve for $θ .$ $θ .$
Solve graphically: $x - 2 \cos x = 5 .$ $x - 2 \cos x = 5 .$
Find the exact value of x: $\cos^{- 1} x = - \tan^{- 1} (- 1) .$ $\cos^{- 1} x = - \tan^{- 1} (- 1) .$

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