Trigonometry Examples

$\sec (30)$

Step 1

The complement of $\sec (30)$ is the angle that when added to $\sec (30)$ forms a right angle ( $90 °$ ).

$90 ° - \sec (30)$

Step 2

Simplify each term.

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Step 2.1

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

Step 2.2

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

Step 2.3

Combine and simplify the denominator.

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Step 2.3.1

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

Step 2.3.2

Raise $\sqrt{3}$ to the power of $1$ .

Step 2.3.3

Raise $\sqrt{3}$ to the power of $1$ .

Step 2.3.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

Step 2.3.5

Add $1$ and $1$ .

Step 2.3.6

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

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Step 2.3.6.1

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

Step 2.3.6.2

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

Step 2.3.6.3

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

Step 2.3.6.4

Cancel the common factor of $2$ .

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Step 2.3.6.4.1

Cancel the common factor.

Step 2.3.6.4.2

Rewrite the expression.

$90 - \frac{2 \sqrt{3}}{3 °}$

Step 2.3.6.5

Evaluate the exponent.

$90 - \frac{2 \sqrt{3}}{3 °}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$90 - \frac{2 \sqrt{3}}{3 °}$

Decimal Form:

$88.84529946 \dots$