Trigonometry Examples

$2 \sin (105) \cos (105)$

Step 1

Apply the sine double-angle identity.

$\sin (2 \cdot 105)$

Step 2

Multiply $2$ by $105$ .

$\sin (210)$

Step 3

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.

$- \sin (30)$

Step 4

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

$- \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{2}$

Decimal Form:

$- 0.5$