What is the value of cos^2((4pi)/3) ?

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

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cos^2((4pi)/3)

cos^{2} (\frac{4 π}{3})

\frac{1}{4}

Solution steps

cos^{2} (\frac{4 π}{3})

Rewrite using trig identities:

\frac{1 + cos ( \frac{2 π}{3} )}{2}

= \frac{1 + cos ( \frac{2 π}{3} )}{2}

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

= \frac{1 - \frac{1}{2}}{2}

Simplify

\frac{1 - \frac{1}{2}}{2} : \frac{1}{4}

= \frac{1}{4}

tan (arcsin (\frac{3}{5}) - arccos (- 1))

\frac{( tan ( 0 ) + 1 ) - ( tan ( - \frac{π}{6} ) + 1 )}{0 + \frac{π}{6}}

sin^{2} (15 0^{\circ})

arctan (tan (\frac{11 π}{9}))

- 2 sin (\frac{3 π}{2})