Trigonometry Examples

\arccos (\cos (\frac{4 π}{3}))

$\arccos (\cos (\frac{4 π}{3}))$

Step 1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the third quadrant.

\arccos (- \cos (\frac{π}{3}))

$\arccos (- \cos (\frac{π}{3}))$

Step 2

The exact value of

\cos (\frac{π}{3})

$\cos (\frac{π}{3})$ is

\frac{1}{2}

$\frac{1}{2}$ .

\arccos (- \frac{1}{2})

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

Step 3

The exact value of

\arccos (- \frac{1}{2})

$\arccos (- \frac{1}{2})$ is

\frac{2 π}{3}

$\frac{2 π}{3}$ .

\frac{2 π}{3}

$\frac{2 π}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{2 π}{3}

$\frac{2 π}{3}$

Decimal Form:

2.09439510 \dots

$2.09439510 \dots$

\arccos (\cos (\frac{4 π}{3}))

$\arccos (\cos (\frac{4 π}{3}))$

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