Precalculus Examples

$\sin (\arcsin (\frac{1}{8})) + \log (1000)$

Step 1

Simplify each term.

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Step 1.1

The functions sine and arcsine are inverses.

$\frac{1}{8} + \log (1000)$

Step 1.2

Logarithm base $10$ of $1000$ is $3$ .

$\frac{1}{8} + 3$

Step 2

To write $3$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{1}{8} + 3 \cdot \frac{8}{8}$

Step 3

Combine $3$ and $\frac{8}{8}$ .

$\frac{1}{8} + \frac{3 \cdot 8}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{1 + 3 \cdot 8}{8}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $8$ .

$\frac{1 + 24}{8}$

Step 5.2

Add $1$ and $24$ .

$\frac{25}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{8}$

Decimal Form:

$3.125$

Mixed Number Form:

$3 \frac{1}{8}$