Trigonometry Examples

$\sqrt{\sec^{2} (\frac{3 π}{4}) - 1}$

Step 1

Apply pythagorean identity.

$\sqrt{\tan^{2} (\frac{3 π}{4})}$

Step 2

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.

$\sqrt{{(- \tan (\frac{π}{4}))}^{2}}$

Step 3

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

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

Step 4

Multiply $- 1$ by $1$ .

$\sqrt{{(- 1)}^{2}}$

Step 5

Raise $- 1$ to the power of $2$ .

$\sqrt{1}$

Step 6

Any root of $1$ is $1$ .

$1$