Trigonometry Examples

$\sin^{2} (30) + \cos^{2} (60)$

Step 1

Simplify each term.

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Step 1.1

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

${(\frac{1}{2})}^{2} + \cos^{2} (60)$

Step 1.2

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

$\frac{1^{2}}{2^{2}} + \cos^{2} (60)$

Step 1.3

One to any power is one.

$\frac{1}{2^{2}} + \cos^{2} (60)$

Step 1.4

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

$\frac{1}{4} + \cos^{2} (60)$

Step 1.5

The exact value of $\cos (60)$ is $\frac{1}{2}$ .

$\frac{1}{4} + {(\frac{1}{2})}^{2}$

Step 1.6

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

$\frac{1}{4} + \frac{1^{2}}{2^{2}}$

Step 1.7

One to any power is one.

$\frac{1}{4} + \frac{1}{2^{2}}$

Step 1.8

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

$\frac{1}{4} + \frac{1}{4}$

$\frac{1}{4} + \frac{1}{4}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{1 + 1}{4}$

Step 2.2

Add $1$ and $1$ .

$\frac{2}{4}$

Step 2.3

Cancel the common factor of $2$ and $4$ .

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Step 2.3.1

Factor $2$ out of $2$ .

$\frac{2 (1)}{4}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $2$ out of $4$ .

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

Step 2.3.2.2

Cancel the common factor.

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

Step 2.3.2.3

Rewrite the expression.

$\frac{1}{2}$

$\frac{1}{2}$

$\frac{1}{2}$

$\frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$