Trigonometry Examples

cot (120)

$\cot (120)$

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cotangent is negative in the second quadrant.

- cot (60)

$- \cot (60)$

The exact value of

cot (60)

$\cot (60)$ is

\frac{1}{\sqrt{3}}

$\frac{1}{\sqrt{3}}$ .

- \frac{1}{\sqrt{3}}

$- \frac{1}{\sqrt{3}}$

Multiply

\frac{1}{\sqrt{3}}

$\frac{1}{\sqrt{3}}$ by

\frac{\sqrt{3}}{\sqrt{3}}

$\frac{\sqrt{3}}{\sqrt{3}}$ .

- (\frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}})

$- (\frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}})$

Combine and simplify the denominator.

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Multiply

\frac{1}{\sqrt{3}}

$\frac{1}{\sqrt{3}}$ by

\frac{\sqrt{3}}{\sqrt{3}}

$\frac{\sqrt{3}}{\sqrt{3}}$ .

- \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}}

$- \frac{\sqrt{3}}{\sqrt{3} \sqrt{3}}$

Raise

\sqrt{3}

$\sqrt{3}$ to the power of

1

$1$ .

- \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}

$- \frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Raise

\sqrt{3}

$\sqrt{3}$ to the power of

1

$1$ .

- \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}

$- \frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

- \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}}

$- \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Add

1

$1$ and

1

$1$ .

- \frac{\sqrt{3}}{{\sqrt{3}}^{2}}

$- \frac{\sqrt{3}}{{\sqrt{3}}^{2}}$

Rewrite

{\sqrt{3}}^{2}

${\sqrt{3}}^{2}$ as

3

$3$ .

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Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{3}

$\sqrt{3}$ as

3^{\frac{1}{2}}

$3^{\frac{1}{2}}$ .

- \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}

$- \frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

- \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}}

$- \frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

- \frac{\sqrt{3}}{3^{\frac{2}{2}}}

$- \frac{\sqrt{3}}{3^{\frac{2}{2}}}$

Cancel the common factor of

2

$2$ .

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Cancel the common factor.

$- \frac{\sqrt{3}}{3^{\frac{2}{2}}}$

Rewrite the expression.

$- \frac{\sqrt{3}}{3^{1}}$

Evaluate the exponent.

$- \frac{\sqrt{3}}{3}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{3}}{3}$

Decimal Form:

$- 0.57735026 \dots$