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Popular >

cos^2(30)

Solution

cos^{2} (3 0^{\circ})

Solution

\frac{3}{4}

+1

Decimal Notation

0.75

Solution steps

cos^{2} (3 0^{\circ})

Use the following trivial identity:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 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{3}{2}

= (\frac{3}{2})^{2}

Simplify

(\frac{3}{2})^{2} : \frac{3}{4}

(\frac{3}{2})^{2}

Apply exponent rule:

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

= \frac{( 3 ) ^{2}}{2 ^{2}}

(3)^{2} : 3

Apply radical rule:

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

= (3^{\frac{1}{2}})^{2}

Apply exponent rule:

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

= 3^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2}

Cancel the common factor:

2

= 1

= 3

= \frac{3}{2 ^{2}}

2^{2} = 4

= \frac{3}{4}

= \frac{3}{4}

Popular Examples

cot(-30)+tan(600)-csc(-450)

cot (- 3 0^{\circ}) + tan (60 0^{\circ}) - csc (- 45 0^{\circ})

cos (\frac{5 π}{4})

cos^{2} (\frac{π}{2})

arcsin((sqrt(3))/2)

arcsin (\frac{3}{2})

prove cos^2(x)-sin^2(x)=1-2sin^2(x)prove

cos^{2} (x) - sin^{2} (x) = 1 - 2 sin^{2} (x)

Frequently Asked Questions (FAQ)

What is the value of cos^2(30) ?
The value of cos^2(30) is 3/4