### Home > APCALC > Chapter 1 > Lesson 1.3.1 > Problem1-104

1-104.

Determine the exact value(s) of $x$ in the domain $0 ≤ x ≤ 2π$ if:

1. $\sin(x) = −\frac { 1 } { 2 }$, $\tan(x) > 0$

$\text{sin}x=\frac{\text{opposite}}{\text{hypotenuse}},\text{ cos}x=\frac{\text{adjacent}}{\text{hypotenuse}},\text{ tan}x=\frac{\text{sin}x}{\text{cos}x}$

In which quadrant of the unit circle is sine negative and tangent positive?

2. $\cot(x)$ is undefined, $\cos(x) > 0$

Refer to the hint in part (a). And recall that cotangent is the reciprocal of tangent.

For $\cot (x)$ to be undefined, its denominator must equal $0$.

3. $\csc(x) = \sqrt { 2 }$, $\sin(x) > \cos(x)$

Refer to the hint in part (a). And recall that cosecant is the reciprocal of sine.

$x=\frac{3\pi}{4}$