Trigonometry Examples

$\arcsin (\sqrt{\frac{2}{2}}) + 0.5 \arctan (- \sqrt{3})$

Step 1

Simplify each term.

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Step 1.1

Divide $2$ by $2$ .

$\arcsin (\sqrt{1}) + 0.5 \arctan (- \sqrt{3})$

Step 1.2

Any root of $1$ is $1$ .

$\arcsin (1) + 0.5 \arctan (- \sqrt{3})$

Step 1.3

The exact value of $\arcsin (1)$ is $\frac{π}{2}$ .

$\frac{π}{2} + 0.5 \arctan (- \sqrt{3})$

Step 1.4

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

$\frac{π}{2} + 0.5 (- \frac{π}{3})$

Step 1.5

Cancel the common factor of $0.5$ .

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Step 1.5.1

Move the leading negative in $- \frac{π}{3}$ into the numerator.

$\frac{π}{2} + 0.5 \frac{- π}{3}$

Step 1.5.2

Factor $0.5$ out of $3$ .

$\frac{π}{2} + 0.5 \frac{- π}{0.5 (6)}$

Step 1.5.3

Cancel the common factor.

$\frac{π}{2} + 0.5 \frac{- π}{0.5 \cdot 6}$

Step 1.5.4

Rewrite the expression.

$\frac{π}{2} + \frac{- π}{6}$

Step 1.6

Move the negative in front of the fraction.

$\frac{π}{2} - \frac{π}{6}$

Step 2

To write $\frac{π}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{π}{2} \cdot \frac{3}{3} - \frac{π}{6}$

Step 3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{π}{2}$ by $\frac{3}{3}$ .

$\frac{π \cdot 3}{2 \cdot 3} - \frac{π}{6}$

Step 3.2

Multiply $2$ by $3$ .

$\frac{π \cdot 3}{6} - \frac{π}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{π \cdot 3 - π}{6}$

Step 5

Simplify the numerator.

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Step 5.1

Move $3$ to the left of $π$ .

$\frac{3 \cdot π - π}{6}$

Step 5.2

Subtract $π$ from $3 π$ .

$\frac{2 π}{6}$

Step 6

Cancel the common factor of $2$ and $6$ .

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Step 6.1

Factor $2$ out of $2 π$ .

$\frac{2 (π)}{6}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $6$ .

$\frac{2 π}{2 \cdot 3}$

Step 6.2.2

Cancel the common factor.

$\frac{2 π}{2 \cdot 3}$

Step 6.2.3

Rewrite the expression.

$\frac{π}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{π}{3}$

Decimal Form:

$1.04719755 \dots$