Trigonometry Examples

$- 2 \sin (\frac{5 π}{4})$

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 $2$ .

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Step 3.1

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

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

Step 3.2

Factor $2$ out of $- 2$ .

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

Step 3.3

Cancel the common factor.

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

Step 3.4

Rewrite the expression.

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

Step 4

Multiply.

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Step 4.1

Multiply $- 1$ by $- 1$ .

$1 \sqrt{2}$

Step 4.2

Multiply $\sqrt{2}$ by $1$ .

$\sqrt{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{2}$

Decimal Form:

$1.41421356 \dots$