Trigonometry Examples

$\frac{150 \sin (150)}{280}$

Step 1

Cancel the common factor of $150$ and $280$ .

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Step 1.1

Factor $10$ out of $150 \sin (150)$ .

$\frac{10 (15 \sin (150))}{280}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $10$ out of $280$ .

$\frac{10 (15 \sin (150))}{10 (28)}$

Step 1.2.2

Cancel the common factor.

$\frac{10 (15 \sin (150))}{10 \cdot 28}$

Step 1.2.3

Rewrite the expression.

$\frac{15 \sin (150)}{28}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\frac{15 \sin (30)}{28}$

Step 2.2

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

$\frac{15 (\frac{1}{2})}{28}$

Step 3

Combine $15$ and $\frac{1}{2}$ .

$\frac{\frac{15}{2}}{28}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{15}{2} \cdot \frac{1}{28}$

Step 5

Multiply $\frac{15}{2} \cdot \frac{1}{28}$ .

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Step 5.1

Multiply $\frac{15}{2}$ by $\frac{1}{28}$ .

$\frac{15}{2 \cdot 28}$

Step 5.2

Multiply $2$ by $28$ .

$\frac{15}{56}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{56}$

Decimal Form:

$0.26785714 \dots$