Trigonometry Examples

$\sin (\frac{\frac{3 π}{2}}{2})$

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Multiply $\frac{3 π}{2} \cdot \frac{1}{2}$ .

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Step 2.1

Multiply $\frac{3 π}{2}$ by $\frac{1}{2}$ .

$\sin (\frac{3 π}{2 \cdot 2})$

Step 2.2

Multiply $2$ by $2$ .

$\sin (\frac{3 π}{4})$

Step 3

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

$\sin (\frac{π}{4})$

Step 4

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{2}}{2}$

Decimal Form:

$0.70710678 \dots$