Trigonometry Examples

$\sin (120) - \sin (90) = \sin (30)$

Step 1

Simplify each term.

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Step 1.1

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

$\sin (60) - \sin (90) = \sin (30)$

Step 1.2

The exact value of $\sin (60)$ is $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{3}}{2} - \sin (90) = \sin (30)$

Step 1.3

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

$\frac{\sqrt{3}}{2} - 1 \cdot 1 = \sin (30)$

Step 1.4

Multiply $- 1$ by $1$ .

$\frac{\sqrt{3}}{2} - 1 = \sin (30)$

Step 2

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

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

Step 3

Since $\frac{\sqrt{3}}{2} - 1 \neq \frac{1}{2}$ , there are no solutions.

No solution