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

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

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cos((-4pi)/3)

cos (\frac{- 4 π}{3})

- \frac{1}{2}

Solution steps

cos (\frac{- 4 π}{3})

Simplify

= cos (- \frac{4 π}{3})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{4 π}{3}) = cos (\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}

arccos (\frac{6}{8})

arcsin (\frac{5}{7})

arctan (tan (\frac{17 π}{3}))

\frac{sin ( 6 0 ^{\circ} )}{cos ( 6 0 ^{\circ} )}

sec (\frac{π}{12})