What is the value of cos^6(pi/2) ?

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cos^6(pi/2)

cos^{6} (\frac{π}{2})

0

Solution steps

cos^{6} (\frac{π}{2})

Use the following trivial identity:

cos (\frac{π}{2}) = 0

cos (\frac{π}{2})

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 0

= 0^{6}

Simplify

= 0

sin (\frac{7 π}{16})

2 cos (- \frac{π}{4}) + \frac{π}{4}

sin (- 8 π)

sin (\frac{π}{2} + 1)

cos (\frac{3 π}{5}) cos (\frac{7 π}{30}) - sin (\frac{3 π}{5}) sin (\frac{7 π}{30})