Precalculus Examples

$- 5 \cos ((\frac{3 π}{2}) - \frac{π}{2})$

Step 1

Combine the numerators over the common denominator.

$- 5 \cos (\frac{3 π - π}{2})$

Step 2

Subtract $π$ from $3 π$ .

$- 5 \cos (\frac{2 π}{2})$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

$- 5 \cos (\frac{2 π}{2})$

Step 3.2

Divide $π$ by $1$ .

$- 5 \cos (π)$

Step 4

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.

$- 5 (- \cos (0))$

Step 5

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

$- 5 (- 1 \cdot 1)$

Step 6

Multiply $- 5 (- 1 \cdot 1)$ .

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Step 6.1

Multiply $- 1$ by $1$ .

$- 5 \cdot - 1$

Step 6.2

Multiply $- 5$ by $- 1$ .

$5$