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Popular >

(cos(pi/3))^2

Solution

(cos (\frac{π}{3}))^{2}

Solution

\frac{1}{4}

+1

Decimal Notation

0.25

Solution steps

(cos (\frac{π}{3}))^{2}

= cos^{2} (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

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}

= \frac{1}{2}

= (\frac{1}{2})^{2}

Simplify

(\frac{1}{2})^{2} : \frac{1}{4}

(\frac{1}{2})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{2 ^{2}}

Apply rule

1^{a} = 1

1^{2} = 1

= \frac{1}{2 ^{2}}

2^{2} = 4

= \frac{1}{4}

= \frac{1}{4}

Popular Examples

arccos (\frac{21}{27})

7(cos((7pi)/6)+isin((7pi)/6))

7 (cos (\frac{7 π}{6}) + i sin (\frac{7 π}{6}))

arccos (0.894)

arctan(sqrt(3))-arctan(0)

arctan (3) - arctan (0)

arcsin (1.66)

Frequently Asked Questions (FAQ)

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