### Home > APCALC > Chapter 1 > Lesson 1.3.2 > Problem1-116

1-116.

Calculus problems often require using one or more of the trigonometric identities to solve problems. Solve each of the following equations on the interval $[0, 2π)$. Use exact values. Homework Help ✎

1. $\tan(x) · \csc(x) = 2$

Simplify the left side of the equation to solve for $x$.

$\text{Remember that tan}x=\frac{\text{sin}x}{\text{cos}x} \text{ and }\text{csc}x=\frac{1}{\text{sin}x}.$

$\frac{\text{sin}x}{\text{cos}x}\cdot\frac{1}{\text{sin}x}=2$;   $\frac{1}{\text{cos}x}=2$;    $\text{cos}x=\frac{1}{2}$

Use the unit circle to solve for $x$.

$\frac{\pi }{3},\ \frac{5\pi }{3}$

1. $\sin(x) · \cos(x) =\frac { 1 } { 4 }$

See part (a).

1. $2\sin^2(x) - \cos(x) - 1 = 0$

See part (a).

1. $\tan(x) + \cot(x) = -2$

See part (a).