Find the Exact Value sin((7pi)/6)-sin(pi/3)

$\sin (\frac{7 π}{6}) - \sin (\frac{π}{3})$

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.

$- \sin (\frac{π}{6}) - \sin (\frac{π}{3})$

Step 2

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

$- \frac{1}{2} - \sin (\frac{π}{3})$

Step 3

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 1.36602540 \dots$

Find the Exact Value sin((7pi)/6)-sin(pi/3)

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