Trigonometry Examples

\csc (330)

$\csc (330)$

Step 1

Find the value using the definition of cosecant.

\csc (330) = \frac{hypotenuse}{opposite}

$\csc (330) = \frac{hypotenuse}{opposite}$

Step 2

Substitute the values into the definition.

\csc (330) = \frac{1}{- \frac{1}{2}}

$\csc (330) = \frac{1}{- \frac{1}{2}}$

Step 3

Simplify the result.

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Step 3.1

Cancel the common factor of

1

$1$ and

- 1

$- 1$ .

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Step 3.1.1

Rewrite

1

$1$ as

- 1 (- 1)

$- 1 (- 1)$ .

\frac{- 1 (- 1)}{- \frac{1}{2}}

$\frac{- 1 (- 1)}{- \frac{1}{2}}$

Step 3.1.2

Move the negative in front of the fraction.

- \frac{1}{\frac{1}{2}}

$- \frac{1}{\frac{1}{2}}$

- \frac{1}{\frac{1}{2}}

$- \frac{1}{\frac{1}{2}}$

Step 3.2

Multiply the numerator by the reciprocal of the denominator.

- (1 \cdot 2)

$- (1 \cdot 2)$

Step 3.3

Multiply

- (1 \cdot 2)

$- (1 \cdot 2)$ .

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Step 3.3.1

Multiply

2

$2$ by

1

$1$ .

- 1 \cdot 2

$- 1 \cdot 2$

Step 3.3.2

Multiply

- 1

$- 1$ by

2

$2$ .

- 2

$- 2$

- 2

$- 2$

- 2

$- 2$

Step 4