Trigonometry Examples

$- 4 \arcsin (x) = π$

Step 1

Divide each term in $- 4 \arcsin (x) = π$ by $- 4$ and simplify.

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Step 1.1

Divide each term in $- 4 \arcsin (x) = π$ by $- 4$ .

$\frac{- 4 \arcsin (x)}{- 4} = \frac{π}{- 4}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $- 4$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{- 4 \arcsin (x)}{- 4} = \frac{π}{- 4}$

Step 1.2.1.2

Divide $\arcsin (x)$ by $1$ .

$\arcsin (x) = \frac{π}{- 4}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Move the negative in front of the fraction.

$\arcsin (x) = - \frac{π}{4}$

Step 2

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

$x = \sin (- \frac{π}{4})$

Step 3

Simplify the right side.

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Step 3.1

Simplify $\sin (- \frac{π}{4})$ .

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Step 3.1.1

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

$x = \sin (\frac{7 π}{4})$

Step 3.1.2

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

$x = - \sin (\frac{π}{4})$

Step 3.1.3

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$x = - \frac{\sqrt{2}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{\sqrt{2}}{2}$

Decimal Form:

$x = - 0.70710678 \dots$