Trigonometry Examples

$\arcsin (x) = 5 π$

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

$x = \sin (5 π)$

Simplify the right side.

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Simplify $\sin (5 π)$ .

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Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$x = \sin (π)$

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$x = \sin (0)$

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

$x = 0$

Exclude the solutions that do not make $\arcsin (x) = 5 π$ true.

$No solution$