Trigonometry Examples

$3 \cos (\frac{5 π}{4})$

Step 1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

$3 (- \cos (\frac{π}{4}))$

Step 2

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

$3 (- \frac{\sqrt{2}}{2})$

Step 3

Multiply $3 (- \frac{\sqrt{2}}{2})$ .

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Step 3.1

Multiply $- 1$ by $3$ .

$- 3 \frac{\sqrt{2}}{2}$

Step 3.2

Combine $- 3$ and $\frac{\sqrt{2}}{2}$ .

$\frac{- 3 \sqrt{2}}{2}$

Step 4

Move the negative in front of the fraction.

$- \frac{3 \sqrt{2}}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{3 \sqrt{2}}{2}$

Decimal Form:

$- 2.12132034 \dots$