Precalculus Examples

$\cos (- \frac{25 π}{4}) - \tan (- \frac{25 π}{4})$

Step 1

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

$\cos (\frac{7 π}{4}) - \tan (- \frac{25 π}{4})$

Step 2

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

$\cos (\frac{π}{4}) - \tan (- \frac{25 π}{4})$

Step 3

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

$\frac{\sqrt{2}}{2} - \tan (- \frac{25 π}{4})$

Step 4

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

$\frac{\sqrt{2}}{2} - \tan (\frac{7 π}{4})$

Step 5

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

$\frac{\sqrt{2}}{2} - - \tan (\frac{π}{4})$

Step 6

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

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

Step 7

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

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Step 7.1

Multiply $- 1$ by $1$ .

$\frac{\sqrt{2}}{2} - - 1$

Step 7.2

Multiply $- 1$ by $- 1$ .

$\frac{\sqrt{2}}{2} + 1$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{2}}{2} + 1$

Decimal Form:

$1.70710678 \dots$