Trigonometry Examples

$\arcsin (x) - \arctan (\frac{\sqrt{3}}{3}) = - \frac{π}{6}$

Step 1

Simplify the left side.

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Step 1.1

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

$\arcsin (x) - \frac{π}{6} = - \frac{π}{6}$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Add $\frac{π}{6}$ to both sides of the equation.

$\arcsin (x) = - \frac{π}{6} + \frac{π}{6}$

Step 2.2

Combine the numerators over the common denominator.

$\arcsin (x) = \frac{- π + π}{6}$

Step 2.3

Add $- π$ and $π$ .

$\arcsin (x) = \frac{0}{6}$

Step 2.4

Divide $0$ by $6$ .

$\arcsin (x) = 0$

Step 3

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

$x = \sin (0)$

Step 4

Simplify the right side.

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Step 4.1

The exact value of $\sin (0)$ is $0$ .

$x = 0$