Trigonometry Examples

\arcsin (\frac{3}{5}) + \arccos (x) = \frac{π}{4}

$\arcsin (\frac{3}{5}) + \arccos (x) = \frac{π}{4}$

Step 1

Simplify the left side.

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Step 1.1

Evaluate

\arcsin (\frac{3}{5})

$\arcsin (\frac{3}{5})$ .

0.6435011 + \arccos (x) = \frac{π}{4}

$0.6435011 + \arccos (x) = \frac{π}{4}$

0.6435011 + \arccos (x) = \frac{π}{4}

$0.6435011 + \arccos (x) = \frac{π}{4}$

Step 2

Move all terms not containing

x

$x$ to the right side of the equation.

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Step 2.1

Subtract

0.6435011

$0.6435011$ from both sides of the equation.

\arccos (x) = \frac{π}{4} - 0.6435011

$\arccos (x) = \frac{π}{4} - 0.6435011$

Step 2.2

Subtract

0.6435011

$0.6435011$ from

\frac{π}{4}

$\frac{π}{4}$ .

\arccos (x) = 0.14189705

$\arccos (x) = 0.14189705$

\arccos (x) = 0.14189705

$\arccos (x) = 0.14189705$

Step 3

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

x

$x$ from inside the arccosine.

x = \cos (0.14189705)

$x = \cos (0.14189705)$

Step 4

The result can be shown in multiple forms.

Exact Form:

x = \cos (0.14189705)

$x = \cos (0.14189705)$

Decimal Form:

x = 0.98994949 \dots

$x = 0.98994949 \dots$