Trigonometry Examples

$\sin (\frac{6 π}{4})$

Step 1

Cancel the common factor of $6$ and $4$ .

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Step 1.1

Factor $2$ out of $6 π$ .

$\sin (\frac{2 (3 π)}{4})$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $4$ .

$\sin (\frac{2 (3 π)}{2 (2)})$

Step 1.2.2

Cancel the common factor.

$\sin (\frac{2 (3 π)}{2 \cdot 2})$

Step 1.2.3

Rewrite the expression.

$\sin (\frac{3 π}{2})$

Step 2

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.

$- \sin (\frac{π}{2})$

Step 3

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

$- 1 \cdot 1$

Step 4

Multiply $- 1$ by $1$ .

$- 1$