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

1-104.

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

1. $\operatorname { sin } x = - \frac { 1 } { 2 } , \operatorname { tan } x > 0$.

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

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

2. cot $x$ is undefined, $\operatorname{cos} x > 0$.

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. $\operatorname { csc } x = \sqrt { 2 } , \operatorname { sin } x > \operatorname { cos } x$.

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