Precalculus Examples

$y = \arctan (\tan (\frac{3 π}{4}))$

Step 1

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 second quadrant.

$y = \arctan (- \tan (\frac{π}{4}))$

Step 2

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

$y = \arctan (- 1 \cdot 1)$

Step 3

Multiply $- 1$ by $1$ .

$y = \arctan (- 1)$

Step 4

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

$y = - \frac{π}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{π}{4}$

Decimal Form:

$y = - 0.78539816 \dots$