Find the Value Using the Unit Circle csc((11pi)/6)

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Trigonometry

$\csc (\frac{11 π}{6})$

Find the value using the definition of cosecant.

$\csc (\frac{11 π}{6}) = \frac{hypotenuse}{opposite}$

Substitute the values into the definition.

$\csc (\frac{11 π}{6}) = \frac{1}{- \frac{1}{2}}$

Simplify the result.

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

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

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

Move the negative in front of the fraction.

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

Multiply the numerator by the reciprocal of the denominator.

$- (1 \cdot 2)$

Multiply $2$ by $1$ .

$- 1 \cdot 2$

Multiply $- 1$ by $2$ .

$- 2$

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