Trigonometry Examples

$\sin (\frac{7 π}{6}) \cos (\frac{π}{6})$

Step 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.

$- \sin (\frac{π}{6}) \cos (\frac{π}{6})$

Step 2

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$- \frac{1}{2} \cos (\frac{π}{6})$

Step 3

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$- \frac{1}{2} \cdot \frac{\sqrt{3}}{2}$

Step 4

Multiply $- \frac{1}{2} \cdot \frac{\sqrt{3}}{2}$ .

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Step 4.1

Multiply $\frac{\sqrt{3}}{2}$ by $\frac{1}{2}$ .

$- \frac{\sqrt{3}}{2 \cdot 2}$

Step 4.2

Multiply $2$ by $2$ .

$- \frac{\sqrt{3}}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{3}}{4}$

Decimal Form:

$- 0.43301270 \dots$