Find the Exact Value sin((5pi)/4)

$\sin (\frac{5 π}{4})$

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.

$- \sin (\frac{π}{4})$

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.70710678 \dots$

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