Find the Exact Value sin(135 degrees )-sin(270 degrees )

$\sin (135 °) - \sin (270 °)$

Step 1

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

$\sin (45) - \sin (270 °)$

Step 2

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

$\frac{\sqrt{2}}{2} - \sin (270 °)$

Step 3

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

$\frac{\sqrt{2}}{2} - - \sin (90)$

Step 4

The exact value of $\sin (90)$ is $1$ .

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

Step 5

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

Multiply $- 1$ by $1$ .

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

Multiply $- 1$ by $- 1$ .

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.70710678 \dots$

Find the Exact Value sin(135 degrees )-sin(270 degrees )

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