What is the value of cos^6(0) ?

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cos^6(0)

cos^{6} (0)

1

Solution steps

cos^{6} (0)

Use the following trivial identity:

cos (0) = 1

cos (0)

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}

= 1

= 1^{6}

Simplify

= 1

\frac{5}{π} - arccos (\frac{50}{110})

4 cos^{2} (6 0^{\circ}) + 3 tan (3 0^{\circ})

cos (π - \frac{π}{3})

\frac{12.2}{sin ( 4 0 ^{\circ} )}

cos (3 0^{\circ}) sin (4 5^{\circ}) + sin (3 0^{\circ}) tan (3 0^{\circ})