Precalculus Examples

$4 \csc (\frac{3 π}{4}) - \cot (- \frac{π}{4})$

Step 1

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

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

Step 2

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

$4 \sqrt{2} - \cot (- \frac{π}{4})$

Step 3

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$4 \sqrt{2} - \cot (\frac{7 π}{4})$

Step 4

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.

$4 \sqrt{2} - - \cot (\frac{π}{4})$

Step 5

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

$4 \sqrt{2} - (- 1 \cdot 1)$

Step 6

Multiply $- (- 1 \cdot 1)$ .

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Step 6.1

Multiply $- 1$ by $1$ .

$4 \sqrt{2} - - 1$

Step 6.2

Multiply $- 1$ by $- 1$ .

$4 \sqrt{2} + 1$

Step 7

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{2} + 1$

Decimal Form:

$6.65685424 \dots$