Trigonometry Examples

$\tan (60) + \tan (150)$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\tan (60)$ is $\sqrt{3}$ .

$\sqrt{3} + \tan (150)$

Step 1.2

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

$\sqrt{3} - \tan (30)$

Step 1.3

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

$\sqrt{3} - \frac{\sqrt{3}}{3}$

Step 2

To write $\sqrt{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\sqrt{3} \cdot \frac{3}{3} - \frac{\sqrt{3}}{3}$

Step 3

Combine fractions.

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Step 3.1

Combine $\sqrt{3}$ and $\frac{3}{3}$ .

$\frac{\sqrt{3} \cdot 3}{3} - \frac{\sqrt{3}}{3}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{\sqrt{3} \cdot 3 - \sqrt{3}}{3}$

Step 4

Simplify the numerator.

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Step 4.1

Move $3$ to the left of $\sqrt{3}$ .

$\frac{3 \cdot \sqrt{3} - \sqrt{3}}{3}$

Step 4.2

Subtract $\sqrt{3}$ from $3 \sqrt{3}$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.15470053 \dots$