Trigonometry Examples

$\sin (225) \sin (30)$

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.

$- \sin (45) \sin (30)$

Step 2

The exact value of $\sin (45)$ is $\frac{\sqrt{2}}{2}$ .

$- \frac{\sqrt{2}}{2} \sin (30)$

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Multiply $2$ by $2$ .

$- \frac{\sqrt{2}}{4}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{2}}{4}$

Decimal Form:

$- 0.35355339 \dots$