Find the Exact Value 2sin((5pi)/4)

$2 \sin (\frac{5 π}{4})$

Step 1

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.

$2 (- \sin (\frac{π}{4}))$

Step 2

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

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

Step 3

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{\sqrt{2}}{2}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

$- \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \sqrt{2}$

Decimal Form:

$- 1.41421356 \dots$

Find the Exact Value 2sin((5pi)/4)

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