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

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

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Find the Exact Value cos((4pi)/3)

cos (\frac{( 4 π )}{3})

- \frac{1}{2}

Solution steps

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}

cos (\frac{( 3 π )}{4})

sec (\frac{( 5 π )}{6})

tan (θ) = \frac{- 4}{5}

sec (\frac{( 5 π )}{3})

sin (x) = \frac{18.5}{20}