Precalculus Examples

$\sin (\frac{4 (3 π)}{2} - 2) \sin (\frac{2 (3 π)}{2})$

Step 1

Simplify each term.

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Step 1.1

Cancel the common factor of $4$ and $2$ .

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Step 1.1.1

Factor $2$ out of $4 (3 π)$ .

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

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $2$ .

$\sin (\frac{2 (2 (3 π))}{2 (1)} - 2) \sin (\frac{2 (3 π)}{2})$

Step 1.1.2.2

Cancel the common factor.

$\sin (\frac{2 (2 (3 π))}{2 \cdot 1} - 2) \sin (\frac{2 (3 π)}{2})$

Step 1.1.2.3

Rewrite the expression.

$\sin (\frac{2 (3 π)}{1} - 2) \sin (\frac{2 (3 π)}{2})$

Step 1.1.2.4

Divide $2 (3 π)$ by $1$ .

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

Step 1.2

Multiply $3$ by $2$ .

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

Step 2

Evaluate $\sin (6 π - 2)$ .

$- 0.90929742 \sin (\frac{2 (3 π)}{2})$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Cancel the common factor.

$- 0.90929742 \sin (\frac{2 (3 π)}{2})$

Step 3.2

Divide $3 π$ by $1$ .

$- 0.90929742 \sin (3 π)$

Step 4

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

$- 0.90929742 \sin (π)$

Step 5

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

$- 0.90929742 \sin (0)$

Step 6

The exact value of $\sin (0)$ is $0$ .

$- 0.90929742 \cdot 0$

Step 7

Multiply $- 0.90929742$ by $0$ .

$0$