Calculus Examples

$3 \cos^{2} (\frac{3 π}{2}) - 6 \sin (\frac{3 π}{2})$

Step 1

Simplify each term.

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Step 1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$3 \cos^{2} (\frac{π}{2}) - 6 \sin (\frac{3 π}{2})$

Step 1.2

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

$3 \cdot 0^{2} - 6 \sin (\frac{3 π}{2})$

Step 1.3

Raising $0$ to any positive power yields $0$ .

$3 \cdot 0 - 6 \sin (\frac{3 π}{2})$

Step 1.4

Multiply $3$ by $0$ .

$0 - 6 \sin (\frac{3 π}{2})$

Step 1.5

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

$0 - 6 (- \sin (\frac{π}{2}))$

Step 1.6

The exact value of $\sin (\frac{π}{2})$ is $1$ .

$0 - 6 (- 1 \cdot 1)$

Step 1.7

Multiply $- 6 (- 1 \cdot 1)$ .

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Step 1.7.1

Multiply $- 1$ by $1$ .

$0 - 6 \cdot - 1$

Step 1.7.2

Multiply $- 6$ by $- 1$ .

$0 + 6$

Step 2

Add $0$ and $6$ .

$6$