Trigonometry Examples

$\sin (\frac{6 π}{2})$

Step 1

Cancel the common factor of $6$ and $2$ .

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Step 1.1

Factor $2$ out of $6 π$ .

$\sin (\frac{2 (3 π)}{2})$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $2$ .

$\sin (\frac{2 (3 π)}{2 (1)})$

Step 1.2.2

Cancel the common factor.

$\sin (\frac{2 (3 π)}{2 \cdot 1})$

Step 1.2.3

Rewrite the expression.

$\sin (\frac{3 π}{1})$

Step 1.2.4

Divide $3 π$ by $1$ .

$\sin (3 π)$

Step 2

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

$\sin (π)$

Step 3

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

$\sin (0)$

Step 4

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

$0$