Precalculus Examples

$y = 2 \sin (- \frac{3 π}{4})$

Step 1

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$y = 2 \sin (\frac{5 π}{4})$

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.

$y = 2 (- \sin (\frac{π}{4}))$

Step 3

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

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

Step 4

Cancel the common factor of $2$ .

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Step 4.1

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

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

Step 4.2

Cancel the common factor.

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

Step 4.3

Rewrite the expression.

$y = - \sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = - \sqrt{2}$

Decimal Form:

$y = - 1.41421356 \dots$