Trigonometry Examples

arccot (\cot (\frac{5 π}{4}))

$arccot (\cot (\frac{5 π}{4}))$

Step 1

To convert degrees to radians, multiply by

\frac{π}{180 °}

$\frac{π}{180 °}$ , since a full circle is

360 °

$360 °$ or

2 π

$2 π$ radians.

Step 2

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

arccot (\cot (\frac{π}{4})) \cdot \frac{π}{180}

$arccot (\cot (\frac{π}{4})) \cdot \frac{π}{180}$ radians

Step 3

The exact value of

\cot (\frac{π}{4})

$\cot (\frac{π}{4})$ is

1

$1$ .

arccot (1) \cdot \frac{π}{180}

$arccot (1) \cdot \frac{π}{180}$ radians

Step 4

The exact value of

arccot (1)

$arccot (1)$ is

\frac{π}{4}

$\frac{π}{4}$ .

\frac{π}{4} \cdot \frac{π}{180}

$\frac{π}{4} \cdot \frac{π}{180}$ radians

Step 5

Multiply

\frac{π}{4} \cdot \frac{π}{180}

$\frac{π}{4} \cdot \frac{π}{180}$ .

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Step 5.1

Multiply

\frac{π}{4}

$\frac{π}{4}$ by

\frac{π}{180}

$\frac{π}{180}$ .

\frac{π π}{4 \cdot 180}

$\frac{π π}{4 \cdot 180}$ radians

Step 5.2

Raise

π

$π$ to the power of

1

$1$ .

\frac{π π}{4 \cdot 180}

$\frac{π π}{4 \cdot 180}$ radians

Step 5.3

Raise

π

$π$ to the power of

1

$1$ .

\frac{π π}{4 \cdot 180}

$\frac{π π}{4 \cdot 180}$ radians

Step 5.4

Use the power rule

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

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

\frac{π^{1 + 1}}{4 \cdot 180}

$\frac{π^{1 + 1}}{4 \cdot 180}$ radians

Step 5.5

Add

1

$1$ and

1

$1$ .

\frac{π^{2}}{4 \cdot 180}

$\frac{π^{2}}{4 \cdot 180}$ radians

Step 5.6

Multiply

4

$4$ by

180

$180$ .

\frac{π^{2}}{720}

$\frac{π^{2}}{720}$ radians

\frac{π^{2}}{720}

$\frac{π^{2}}{720}$ radians