Trigonometry Examples

$\sin (\arcsin (0) - \arccos (\frac{1}{2}))$

Step 1

Simplify each term.

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Step 1.1

The exact value of $\arcsin (0)$ is $0$ .

$\sin (0 - \arccos (\frac{1}{2}))$

Step 1.2

The exact value of $\arccos (\frac{1}{2})$ is $\frac{π}{3}$ .

$\sin (0 - \frac{π}{3})$

Step 2

Subtract $\frac{π}{3}$ from $0$ .

$\sin (- \frac{π}{3})$

Step 3

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\sin (\frac{5 π}{3})$

Step 4

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 fourth quadrant.

$- \sin (\frac{π}{3})$

Step 5

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

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.86602540 \dots$