Trigonometry Examples

$\arccos (x) = \arccos (\frac{7}{25} - \arcsin (\frac{24}{25}))$

Step 1

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

$x = \cos (\arccos (\frac{7}{25} - \arcsin (\frac{24}{25})))$

Step 2

Simplify the right side.

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Step 2.1

Simplify $\cos (\arccos (\frac{7}{25} - \arcsin (\frac{24}{25})))$ .

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Step 2.1.1

The functions cosine and arccosine are inverses.

$x = \frac{7}{25} - \arcsin (\frac{24}{25})$

Step 2.1.2

Simplify each term.

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Step 2.1.2.1

Evaluate $\arcsin (\frac{24}{25})$ .

$x = \frac{7}{25} - 1 \cdot 1.28700221$

Step 2.1.2.2

Multiply $- 1$ by $1.28700221$ .

$x = \frac{7}{25} - 1.28700221$

Step 2.1.3

To write $- 1.28700221$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$x = \frac{7}{25} - 1.28700221 \cdot \frac{25}{25}$

Step 2.1.4

Combine fractions.

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Step 2.1.4.1

Combine $- 1.28700221$ and $\frac{25}{25}$ .

$x = \frac{7}{25} + \frac{- 1.28700221 \cdot 25}{25}$

Step 2.1.4.2

Combine the numerators over the common denominator.

$x = \frac{7 - 1.28700221 \cdot 25}{25}$

Step 2.1.5

Simplify the numerator.

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Step 2.1.5.1

Multiply $- 1.28700221$ by $25$ .

$x = \frac{7 - 32.17505543}{25}$

Step 2.1.5.2

Subtract $32.17505543$ from $7$ .

$x = \frac{- 25.17505543}{25}$

Step 2.1.6

Divide $- 25.17505543$ by $25$ .

$x = - 1.00700221$

Step 3

Exclude the solutions that do not make $\arccos (x) = \arccos (\frac{7}{25} - \arcsin (\frac{24}{25}))$ true.

$No solution$