Trigonometry Examples

$5 \arcsin (x) - 2 π = 2 \arcsin (x) - 3 π$

Step 1

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 1.1

Subtract $2 \arcsin (x)$ from both sides of the equation.

$5 \arcsin (x) - 2 π - 2 \arcsin (x) = - 3 π$

Step 1.2

Subtract $2 \arcsin (x)$ from $5 \arcsin (x)$ .

$3 \arcsin (x) - 2 π = - 3 π$

Step 2

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

Tap for more steps...

Step 2.1

Add $2 π$ to both sides of the equation.

$3 \arcsin (x) = - 3 π + 2 π$

Step 2.2

Add $- 3 π$ and $2 π$ .

$3 \arcsin (x) = - π$

Step 3

Divide each term in $3 \arcsin (x) = - π$ by $3$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $3 \arcsin (x) = - π$ by $3$ .

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

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

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

$\arcsin (x) = \frac{- π}{3}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Move the negative in front of the fraction.

$\arcsin (x) = - \frac{π}{3}$

Step 4

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

$x = \sin (- \frac{π}{3})$

Step 5

Simplify the right side.

Tap for more steps...

Step 5.1

Simplify $\sin (- \frac{π}{3})$ .

Tap for more steps...

Step 5.1.1

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

$x = \sin (\frac{5 π}{3})$

Step 5.1.2

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.

$x = - \sin (\frac{π}{3})$

Step 5.1.3

The exact value of $\sin (\frac{π}{3})$ is $\frac{\sqrt{3}}{2}$ .

$x = - \frac{\sqrt{3}}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{\sqrt{3}}{2}$

Decimal Form:

$x = - 0.86602540 \dots$