Trigonometry Examples

$\frac{1}{2} \cdot (\sin (123 + 102)) + \sin (123 - 102)$

Step 1

Add $123$ and $102$ .

$\frac{1}{2} \cdot \sin (225) + \sin (123 - 102)$

Step 2

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.

$\frac{1}{2} \cdot (- \sin (45)) + \sin (123 - 102)$

Step 3

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

$\frac{1}{2} \cdot (- \frac{\sqrt{2}}{2}) + \sin (123 - 102)$

Step 4

Multiply $\frac{1}{2} (- \frac{\sqrt{2}}{2})$ .

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Step 4.1

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

$- \frac{\sqrt{2}}{2 \cdot 2} + \sin (123 - 102)$

Step 4.2

Multiply $2$ by $2$ .

$- \frac{\sqrt{2}}{4} + \sin (123 - 102)$

Step 5

Subtract $102$ from $123$ .

$- \frac{\sqrt{2}}{4} + \sin (21)$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{2}}{4} + \sin (21)$

Decimal Form:

$0.00481455 \dots$