Trigonometry Examples

$arccot (\cot (\frac{5 π}{4}))$

Step 1

To convert degrees to radians, multiply by $\frac{π}{180 °}$ , since a full circle is $360 °$ or $2 π$ radians.

Step 2

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

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

Step 3

The exact value of $\cot (\frac{π}{4})$ is $1$ .

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

Step 4

The exact value of $arccot (1)$ is $\frac{π}{4}$ .

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

Step 5

Multiply $\frac{π}{4} \cdot \frac{π}{180}$ .

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Step 5.1

Multiply $\frac{π}{4}$ by $\frac{π}{180}$ .

$\frac{π π}{4 \cdot 180}$ radians

Step 5.2

Raise $π$ to the power of $1$ .

$\frac{π π}{4 \cdot 180}$ radians

Step 5.3

Raise $π$ to the power of $1$ .

$\frac{π π}{4 \cdot 180}$ radians

Step 5.4

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

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

Step 5.5

Add $1$ and $1$ .

$\frac{π^{2}}{4 \cdot 180}$ radians

Step 5.6

Multiply $4$ by $180$ .

$\frac{π^{2}}{720}$ radians