Find the Exact Value sin((7pi)/6)^2

$\sin^{2} (\frac{7 π}{6})$

Step 1

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 third quadrant.

${(- \sin (\frac{π}{6}))}^{2}$

Step 2

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

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

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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

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

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

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

Step 4

Raise $- 1$ to the power of $2$ .

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

Step 5

Multiply $\frac{1^{2}}{2^{2}}$ by $1$ .

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

Step 6

One to any power is one.

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

Step 7

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

$\frac{1}{4}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{4}$

Decimal Form:

$0.25$

Find the Exact Value sin((7pi)/6)^2

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