Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

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

$\frac{1}{2} - \sin (\frac{3 π}{2})$

Step 1.2

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 fourth quadrant.

$\frac{1}{2} - - \sin (\frac{π}{2})$

Step 1.3

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

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

Step 1.4

Multiply $- (- 1 \cdot 1)$ .

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Step 1.4.1

Multiply $- 1$ by $1$ .

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

Step 1.4.2

Multiply $- 1$ by $- 1$ .

$\frac{1}{2} + 1$

Step 2

Simplify the expression.

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Step 2.1

Write $1$ as a fraction with a common denominator.

$\frac{1}{2} + \frac{2}{2}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{1 + 2}{2}$

Step 2.3

Add $1$ and $2$ .

$\frac{3}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{2}$

Decimal Form:

$1.5$

Mixed Number Form:

$1 \frac{1}{2}$