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Popular >

cos^4(pi)

Solution

cos^{4} (π)

Solution

1

Solution steps

cos^{4} (π)

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

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)^{4}

Simplify

(- 1)^{4} : 1

(- 1)^{4}

Apply exponent rule:

(- a)^{n} = a^{n},

if

n

is even

(- 1)^{4} = 1^{4}

= 1^{4}

Apply rule

1^{a} = 1

= 1

= 1

Popular Examples

3 sec^{2} (0)

8 cos (\frac{π}{4})

8 cos (\frac{π}{2})

arccos(sin(pi/4))

arccos (sin (\frac{π}{4}))

3 sin (\frac{2 π}{3})

Frequently Asked Questions (FAQ)

What is the value of cos^4(pi) ?
The value of cos^4(pi) is 1