Trigonometry Examples

$\cos (θ) = - \frac{1}{2}$

Step 1

To find the value of $\sec (θ)$ , use the fact that $\frac{1}{\cos (θ)}$ then substitute in the known values.

$\sec (θ) = \frac{1}{\cos (θ)} = \frac{1}{- \frac{1}{2}}$

Step 2

Simplify the result.

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Step 2.1

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

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Step 2.1.1

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

$\sec (θ) = \frac{1}{\cos (θ)} = \frac{- 1 \cdot - 1}{- \frac{1}{2}}$

Step 2.1.2

Move the negative in front of the fraction.

$\sec (θ) = \frac{1}{\cos (θ)} = - \frac{1}{\frac{1}{2}}$

Step 2.2

Multiply the numerator by the reciprocal of the denominator.

$\sec (θ) = \frac{1}{\cos (θ)} = - (1 \cdot 2)$

Step 2.3

Multiply $- (1 \cdot 2)$ .

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Step 2.3.1

Multiply $2$ by $1$ .

$\sec (θ) = \frac{1}{\cos (θ)} = - 1 \cdot 2$

Step 2.3.2

Multiply $- 1$ by $2$ .

$\sec (θ) = \frac{1}{\cos (θ)} = - 2$