Trigonometry Examples

$\arctan (\frac{x}{6}) = 60$

Step 1

Take the inverse arctangent of both sides of the equation to extract $x$ from inside the arctangent.

$\frac{x}{6} = \tan (60)$

Step 2

Simplify the right side.

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Step 2.1

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

$\frac{x}{6} = \sqrt{3}$

Step 3

Multiply both sides of the equation by $6$ .

$6 \frac{x}{6} = 6 \sqrt{3}$

Step 4

Simplify the left side.

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Step 4.1

Cancel the common factor of $6$ .

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Step 4.1.1

Cancel the common factor.

$6 \frac{x}{6} = 6 \sqrt{3}$

Step 4.1.2

Rewrite the expression.

$x = 6 \sqrt{3}$

Step 5

Exclude the solutions that do not make $\arctan (\frac{x}{6}) = 60$ true.

$No solution$