What is the value of cos((-5pi)/3) ?

The value of cos((-5pi)/3) is 1/2

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cos((-5pi)/3)

cos (\frac{- 5 π}{3})

\frac{1}{2}

Solution steps

cos (\frac{- 5 π}{3})

Simplify

= cos (- \frac{5 π}{3})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{5 π}{3}) = cos (\frac{5 π}{3})

= cos (\frac{5 π}{3})

Rewrite using trig identities:

cos (π) cos (\frac{2 π}{3}) - sin (π) sin (\frac{2 π}{3})

= cos (π) cos (\frac{2 π}{3}) - sin (π) sin (\frac{2 π}{3})

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

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

Simplify

= \frac{1}{2}

sin (2 arcsin (- \frac{2}{2}))

2 cos (0) + sin (0)

\frac{tan ( - \frac{2 π}{3} )}{sin ( \frac{7 π}{4} )} - sec (- π)

tan (- \frac{5 π}{8})

arcsin (tan (4 5^{\circ}))