Find the Exact Value sin(585 degrees )

$\sin (585 °)$

Step 1

Remove full rotations of $360$ ° until the angle is between $0$ ° and $360$ °.

$\sin (225)$

Step 2

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.

$- \sin (45)$

Step 3

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.70710678 \dots$

Find the Exact Value sin(585 degrees )

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