Precalculus Examples

$\frac{\cos (- 7 π)}{2}$

Step 1

Simplify the numerator.

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Step 1.1

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\frac{\cos (π)}{2}$

Step 1.2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$\frac{- \cos (0)}{2}$

Step 1.3

The exact value of $\cos (0)$ is $1$ .

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

Step 1.4

Multiply $- 1$ by $1$ .

$\frac{- 1}{2}$

Step 2

Move the negative in front of the fraction.

$- \frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$