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Popular >

cos^2(120)

Solution

cos^{2} (12 0^{\circ})

Solution

\frac{1}{4}

+1

Decimal Notation

0.25

Solution steps

cos^{2} (12 0^{\circ})

Use the following trivial identity:

cos (12 0^{\circ}) = - \frac{1}{2}

cos (12 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} 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:

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

if

n

is even

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

= (\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

tan (3 9^{\circ})

4 sin (\frac{π}{3})

tan (4 2^{\circ})

cos (53.1 3^{\circ})

arccos(cos((6pi)/7))

arccos (cos (\frac{6 π}{7}))

Frequently Asked Questions (FAQ)

What is the value of cos^2(120) ?
The value of cos^2(120) is 1/4