Trigonometry Examples

$\arccos (\frac{1}{- \sqrt{2}})$

Cancel the common factor of $1$ and $- 1$ .

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Rewrite $1$ as $- 1 (- 1)$ .

$\arccos (\frac{- 1 (- 1)}{- \sqrt{2}})$

Move the negative in front of the fraction.

$\arccos (- \frac{1}{\sqrt{2}})$

Multiply $\frac{1}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\arccos (- (\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}}))$

Combine and simplify the denominator.

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Multiply $\frac{1}{\sqrt{2}}$ by $\frac{\sqrt{2}}{\sqrt{2}}$ .

$\arccos (- \frac{\sqrt{2}}{\sqrt{2} \sqrt{2}})$

Raise $\sqrt{2}$ to the power of $1$ .

$\arccos (- \frac{\sqrt{2}}{{\sqrt{2}}^{1} \sqrt{2}})$

Raise $\sqrt{2}$ to the power of $1$ .

$\arccos (- \frac{\sqrt{2}}{{\sqrt{2}}^{1} {\sqrt{2}}^{1}})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\arccos (- \frac{\sqrt{2}}{{\sqrt{2}}^{1 + 1}})$

Add $1$ and $1$ .

$\arccos (- \frac{\sqrt{2}}{{\sqrt{2}}^{2}})$

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$\arccos (- \frac{\sqrt{2}}{{(2^{\frac{1}{2}})}^{2}})$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\arccos (- \frac{\sqrt{2}}{2^{\frac{1}{2} \cdot 2}})$

Combine $\frac{1}{2}$ and $2$ .

$\arccos (- \frac{\sqrt{2}}{2^{\frac{2}{2}}})$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\arccos (- \frac{\sqrt{2}}{2^{\frac{2}{2}}})$

Rewrite the expression.

$\arccos (- \frac{\sqrt{2}}{2^{1}})$

Evaluate the exponent.

$\arccos (- \frac{\sqrt{2}}{2})$

The exact value of $\arccos (- \frac{\sqrt{2}}{2})$ is $\frac{3 π}{4}$ .

$\frac{3 π}{4}$

The result can be shown in multiple forms.

Exact Form:

$\frac{3 π}{4}$

Decimal Form:

$2.35619449 \dots$