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

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

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cos(((-5*pi))/3)

cos (\frac{( - 5 \cdot π )}{3})

\frac{1}{2}

Solution steps

cos (\frac{( - 5 π )}{3})

= 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}

arctan (0.675)

cos (\frac{27}{8} π)

\frac{28}{cos ( 4 5 ^{\circ} )}

arctan (\frac{9}{23})

sec (π) \cdot tan (π)