Algebra Examples

$\sec (\frac{4 π}{3})$

Step 1

Find the value using the definition of secant.

$\sec (\frac{4 π}{3}) = \frac{hypotenuse}{adjacent}$

Step 2

Substitute the values into the definition.

$\sec (\frac{4 π}{3}) = \frac{1}{- \frac{1}{2}}$

Step 3

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 $- (1 \cdot 2)$ .

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Multiply $2$ by $1$ .

$- 1 \cdot 2$

Multiply $- 1$ by $2$ .

$- 2$

Step 4