Trigonometry Examples

$5 \cos (- \frac{2 π}{3})$

Step 1

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

$5 \cos (\frac{4 π}{3})$

Step 2

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.

$5 (- \cos (\frac{π}{3}))$

Step 3

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$5 (- \frac{1}{2})$

Step 4

Multiply $5 (- \frac{1}{2})$ .

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Step 4.1

Multiply $- 1$ by $5$ .

$- 5 (\frac{1}{2})$

Step 4.2

Combine $- 5$ and $\frac{1}{2}$ .

$\frac{- 5}{2}$

Step 5

Move the negative in front of the fraction.

$- \frac{5}{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{2}$

Decimal Form:

$- 2.5$

Mixed Number Form:

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