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MakcuM [25]
3 years ago
7

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

Mathematics
1 answer:
qaws [65]3 years ago
7 0

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)

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