Trigonometry Examples

$\sin (θ) = - \frac{2}{5}$

Step 1

To find the value of $\csc (θ)$ , use the fact that $\frac{1}{\sin (θ)}$ then substitute in the known values.

$\csc (θ) = \frac{1}{\sin (θ)} = \frac{1}{- \frac{2}{5}}$

Step 2

Simplify the result.

Tap for more steps...

Step 2.1

Cancel the common factor of $1$ and $- 1$ .

Tap for more steps...

Step 2.1.1

Rewrite $1$ as $- 1 (- 1)$ .

$\csc (θ) = \frac{1}{\sin (θ)} = \frac{- 1 \cdot - 1}{- \frac{2}{5}}$

Step 2.1.2

Move the negative in front of the fraction.

$\csc (θ) = \frac{1}{\sin (θ)} = - \frac{1}{\frac{2}{5}}$

Step 2.2

Multiply the numerator by the reciprocal of the denominator.

$\csc (θ) = \frac{1}{\sin (θ)} = - (1 (\frac{5}{2}))$

Step 2.3

Multiply $\frac{5}{2}$ by $1$ .

$\csc (θ) = \frac{1}{\sin (θ)} = - \frac{5}{2}$