Trigonometry Examples

$2 \sin^{2} (135)$

Step 1

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

$2 \sin^{2} (45)$

Step 2

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Cancel the common factor of $2$ .

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Step 4.4.1

Cancel the common factor.

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

Step 4.4.2

Rewrite the expression.

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

Step 4.5

Evaluate the exponent.

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

Step 5

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

$2 (\frac{2}{4})$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $4$ .

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

Step 6.2

Cancel the common factor.

$2 \frac{2}{2 \cdot 2}$

Step 6.3

Rewrite the expression.

$\frac{2}{2}$

Step 7

Divide $2$ by $2$ .

$1$