Trigonometry Examples

\arcsin (\frac{5}{13}) + \arccos (x) = \frac{π}{4}

$\arcsin (\frac{5}{13}) + \arccos (x) = \frac{π}{4}$

Step 1

Simplify the left side.

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Step 1.1

Evaluate

\arcsin (\frac{5}{13})

$\arcsin (\frac{5}{13})$ .

0.39479111 + \arccos (x) = \frac{π}{4}

$0.39479111 + \arccos (x) = \frac{π}{4}$

0.39479111 + \arccos (x) = \frac{π}{4}

$0.39479111 + \arccos (x) = \frac{π}{4}$

Step 2

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 2.1

Subtract

0.39479111

$0.39479111$ from both sides of the equation.

\arccos (x) = \frac{π}{4} - 0.39479111

$\arccos (x) = \frac{π}{4} - 0.39479111$

Step 2.2

Subtract

0.39479111

$0.39479111$ from

\frac{π}{4}

$\frac{π}{4}$ .

\arccos (x) = 0.39060704

$\arccos (x) = 0.39060704$

\arccos (x) = 0.39060704

$\arccos (x) = 0.39060704$

Step 3

Take the inverse arccosine of both sides of the equation to extract

x

$x$ from inside the arccosine.

x = \cos (0.39060704)

$x = \cos (0.39060704)$

Step 4

The result can be shown in multiple forms.

Exact Form:

x = \cos (0.39060704)

$x = \cos (0.39060704)$

Decimal Form:

x = 0.92467809 \dots

$x = 0.92467809 \dots$