What is the value of cos(4 pi/3) ?

The value of cos(4 pi/3) is -1/2

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cos(4 pi/3)

cos (4 \frac{π}{3})

- \frac{1}{2}

Solution steps

cos (4 \cdot \frac{π}{3})

Simplify:

4 \cdot \frac{π}{3} = \frac{4 π}{3}

= cos (\frac{4 π}{3})

Rewrite using trig identities:

cos (π) cos (\frac{π}{3}) - sin (π) sin (\frac{π}{3})

= cos (π) cos (\frac{π}{3}) - sin (π) sin (\frac{π}{3})

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

sin (\frac{π}{3}) = \frac{3}{2}

= (- 1) \frac{1}{2} - 0 \cdot \frac{3}{2}

Simplify

= - \frac{1}{2}

sin (arccos (0.8))

cos (2 arcsin (\frac{1}{4}))

arccos (\frac{50}{85})

\frac{10}{cos ( 2 0 ^{\circ} )}

cot (- \frac{9 π}{4})