Question

Express csc(-330) as a trigonometric function of an angle in Quadrant I

Answer 1

Answer:

$\csc(30\degree)$

Step-by-step explanation:

The given trigonometric expression is

$\csc(-330\degree)$

Recall that;

$\csc(\theta)=\frac{1}{\sin(\theta)}$

This implies that;

$\csc(-330\degree)=\frac{1}{\sin(-330)}$

Recall again that;

$\sin(-\theta)=-\sin(\theta)$

We apply this property to get;

$\csc(-330\degree)=-\frac{1}{\sin(330)}$

Finally, we apply the following property of the sine function to get;

$\sin(360\degree-\theta)=-\sin(\theta)$

$\csc(-330\degree)=-\frac{1}{\sin(360\degree-30\degree)}$

$\csc(-330\degree)=-\frac{1}{-\sin(30\degree)}$

$\Rightarrow \csc(-330\degree)=\frac{1}{\sin(30\degree)}$

We rewrite using reciprocal ratios to get;

$\Rightarrow \csc(-330\degree)=\csc(30)$