Precalculus Examples

$8 \cos (5 π + \frac{3 π}{2})$

Step 1

To write $5 π$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$8 \cos (5 π \cdot \frac{2}{2} + \frac{3 π}{2})$

Step 2

Combine fractions.

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Step 2.1

Combine $5 π$ and $\frac{2}{2}$ .

$8 \cos (\frac{5 π \cdot 2}{2} + \frac{3 π}{2})$

Step 2.2

Combine the numerators over the common denominator.

$8 \cos (\frac{5 π \cdot 2 + 3 π}{2})$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $2$ by $5$ .

$8 \cos (\frac{10 π + 3 π}{2})$

Step 3.2

Add $10 π$ and $3 π$ .

$8 \cos (\frac{13 π}{2})$

Step 4

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

$8 \cos (\frac{π}{2})$

Step 5

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$8 \cdot 0$

Step 6

Multiply $8$ by $0$ .

$0$