Find the Exact Value cos(150 degrees )^2

$\cos^{2} (150 °)$

Step 1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

${(- \cos (30))}^{2}$

Step 2

The exact value of $\cos (30)$ is $\frac{\sqrt{3}}{2}$ .

${(- \frac{\sqrt{3}}{2})}^{2}$

Step 3

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

Apply the product rule to $- \frac{\sqrt{3}}{2}$ .

${(- 1)}^{2} {(\frac{\sqrt{3}}{2})}^{2}$

Apply the product rule to $\frac{\sqrt{3}}{2}$ .

${(- 1)}^{2} \frac{{\sqrt{3}}^{2}}{2^{2}}$

Step 4

Simplify the expression.

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

$1 \frac{{\sqrt{3}}^{2}}{2^{2}}$

Multiply $\frac{{\sqrt{3}}^{2}}{2^{2}}$ by $1$ .

$\frac{{\sqrt{3}}^{2}}{2^{2}}$

Step 5

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{{(3^{\frac{1}{2}})}^{2}}{2^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{3^{\frac{1}{2} \cdot 2}}{2^{2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{3^{\frac{2}{2}}}{2^{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3^{\frac{2}{2}}}{2^{2}}$

Rewrite the expression.

$\frac{3^{1}}{2^{2}}$

Evaluate the exponent.

$\frac{3}{2^{2}}$

Step 6

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

$\frac{3}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{4}$

Decimal Form:

$0.75$

Find the Exact Value cos(150 degrees )^2

Related Questions

Support LCMGCF.com by disabling your adblocker.