Precalculus Examples

$\sin (135) = - \frac{\sqrt{2}}{2}$

Step 1

Simplify.

Tap for more steps...

Step 1.1

Divide each term in $\sin (135) = - \frac{\sqrt{2}}{2}$ by $- 1$ .

$\frac{\sin (135)}{- 1} = \frac{- \frac{\sqrt{2}}{2}}{- 1}$

Step 1.2

Move the negative one from the denominator of $\frac{\sin (135)}{- 1}$ .

$- 1 \cdot \sin (135)$

Step 1.3

Rewrite $- 1 \cdot \sin (135)$ as $- \sin (135)$ .

$- \sin (135)$

Step 1.4

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

$- \sin (45)$

Step 1.5

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

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

Step 1.6

Reduce by cancelling the common factors.

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

Step 2

Convert the exponential equation to a logarithmic equation using the logarithm base $(2)$ of the left side $(- \frac{2^{\frac{1}{2}}}{2})$ equals the exponent $(\frac{1}{2})$ .

$\log_{2} (- \frac{2^{\frac{1}{2}}}{2}) = \frac{1}{2}$