Find the Exact Value sin(150)^2

$\sin^{2} (150)$

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

$\sin^{2} (30)$

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

${(\frac{1}{2})}^{2}$

Apply the product rule to $\frac{1}{2}$ .

$\frac{1^{2}}{2^{2}}$

One to any power is one.

$\frac{1}{2^{2}}$

Raise $2$ to the power of $2$ .

$\frac{1}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$