Trigonometry Examples

$\sin (\frac{3 π}{2}) + \cos (\frac{2 π}{3})$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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 fourth quadrant.

$- \sin (\frac{π}{2}) + \cos (\frac{2 π}{3})$

Step 1.2

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

$- 1 \cdot 1 + \cos (\frac{2 π}{3})$

Step 1.3

Multiply $- 1$ by $1$ .

$- 1 + \cos (\frac{2 π}{3})$

Step 1.4

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 second quadrant.

$- 1 - \cos (\frac{π}{3})$

Step 1.5

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

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

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 3

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $- 1$ by $2$ .

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

Step 5.2

Subtract $1$ from $- 2$ .

$\frac{- 3}{2}$

Step 6

Move the negative in front of the fraction.

$- \frac{3}{2}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{2}$

Decimal Form:

$- 1.5$

Mixed Number Form:

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