Find the Exact Value cos(arccos(2/3)-arcsin(-1/3))

$\cos (\arccos (\frac{2}{3}) - \arcsin (- \frac{1}{3}))$

Step 1

Simplify each term.

Evaluate $\arccos (\frac{2}{3})$ .

$\cos (0.84106867 - \arcsin (- \frac{1}{3}))$

Evaluate $\arcsin (- \frac{1}{3})$ .

$\cos (0.84106867 - - 0.3398369)$

Multiply $- 1$ by $- 0.3398369$ .

$\cos (0.84106867 + 0.3398369)$

Step 2

Add $0.84106867$ and $0.3398369$ .

$\cos (1.18090558)$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\cos (\arccos (\frac{2}{3}) - \arcsin (- \frac{1}{3}))$

Decimal Form:

$0.38008736 \dots$