Trigonometry Examples

$\cot (\frac{7 π}{4}) - \cot (\frac{5 π}{4})$

Step 1

Simplify each term.

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Step 1.1

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 fourth quadrant.

$- \cot (\frac{π}{4}) - \cot (\frac{5 π}{4})$

Step 1.2

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

$- 1 \cdot 1 - \cot (\frac{5 π}{4})$

Step 1.3

Multiply $- 1$ by $1$ .

$- 1 - \cot (\frac{5 π}{4})$

Step 1.4

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

$- 1 - \cot (\frac{π}{4})$

Step 1.5

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

$- 1 - 1 \cdot 1$

Step 1.6

Multiply $- 1$ by $1$ .

$- 1 - 1$

Step 2

Subtract $1$ from $- 1$ .

$- 2$