Trigonometry Examples

$6 \tan (\frac{π}{4}) + \sin (\frac{π}{3}) \sec (\frac{π}{6})$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\tan (\frac{π}{4})$ is $1$ .

$6 \cdot 1 + \sin (\frac{π}{3}) \sec (\frac{π}{6})$

Step 1.2

Multiply $6$ by $1$ .

$6 + \sin (\frac{π}{3}) \sec (\frac{π}{6})$

Step 1.3

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

$6 + \frac{\sqrt{3}}{2} \sec (\frac{π}{6})$

Step 1.4

The exact value of $\sec (\frac{π}{6})$ is $\frac{2}{\sqrt{3}}$ .

$6 + \frac{\sqrt{3}}{2} \cdot \frac{2}{\sqrt{3}}$

Step 1.5

Cancel the common factor of $\sqrt{3}$ .

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Step 1.5.1

Cancel the common factor.

$6 + \frac{\sqrt{3}}{2} \cdot \frac{2}{\sqrt{3}}$

Step 1.5.2

Rewrite the expression.

$6 + \frac{1}{2} \cdot 2$

Step 1.6

Cancel the common factor of $2$ .

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Step 1.6.1

Cancel the common factor.

$6 + \frac{1}{2} \cdot 2$

Step 1.6.2

Rewrite the expression.

$6 + 1$

Step 2

Add $6$ and $1$ .

$7$