Trigonometry Examples

$\frac{\sin (30) \cos (60)}{\sin (270)}$

Step 1

Simplify the numerator.

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Step 1.1

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$\frac{\frac{1}{2} \cos (60)}{\sin (270)}$

Step 1.2

The exact value of $\cos (60)$ is $\frac{1}{2}$ .

$\frac{\frac{1}{2} \cdot \frac{1}{2}}{\sin (270)}$

Step 2

Simplify the denominator.

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Step 2.1

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.

$\frac{\frac{1}{2} \cdot \frac{1}{2}}{- \sin (90)}$

Step 2.2

The exact value of $\sin (90)$ is $1$ .

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

Step 2.3

Multiply $- 1$ by $1$ .

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

Step 3

Combine fractions.

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Step 3.1

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

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

Step 3.2

Simplify the expression.

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Step 3.2.1

Multiply $2$ by $2$ .

$\frac{\frac{1}{4}}{- 1}$

Step 3.2.2

Move the negative one from the denominator of $\frac{\frac{1}{4}}{- 1}$ .

$- 1 \cdot \frac{1}{4}$

Step 3.2.3

Rewrite $- 1 (\frac{1}{4})$ as $- (\frac{1}{4})$ .

$- \frac{1}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{4}$

Decimal Form:

$- 0.25$