What is the value of cos^2(60)*44.8 ?

The value of cos^2(60)*44.8 is 56/5

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cos^2(60)*44.8

cos^{2} (6 0^{\circ}) \cdot 44.8

\frac{56}{5}

Decimal Notation

11.2

Solution steps

cos^{2} (6 0^{\circ}) \cdot 44.8

= cos^{2} (6 0^{\circ}) \frac{224}{5}

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 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} \frac{224}{5}

Simplify

(\frac{1}{2})^{2} \frac{224}{5} : \frac{56}{5}

(\frac{1}{2})^{2} \frac{224}{5}

(\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}}

= \frac{224}{5} \cdot \frac{1}{2 ^{2}}

Multiply fractions:

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

= \frac{1 \cdot 224}{2 ^{2} \cdot 5}

Multiply the numbers:

1 \cdot 224 = 224

= \frac{224}{2 ^{2} \cdot 5}

Factor

224 : 2^{5} \cdot 7

Factor

224 = 2^{5} \cdot 7

= \frac{2 ^{5} \cdot 7}{2 ^{2} \cdot 5}

Cancel

\frac{2 ^{5} \cdot 7}{2 ^{2} \cdot 5} : \frac{2 ^{3} \cdot 7}{5}

\frac{2 ^{5} \cdot 7}{2 ^{2} \cdot 5}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{2 ^{5}}{2 ^{2}} = 2^{5 - 2}

= \frac{7 \cdot 2 ^{5 - 2}}{5}

Subtract the numbers:

5 - 2 = 3

= \frac{2 ^{3} \cdot 7}{5}

= \frac{2 ^{3} \cdot 7}{5}

2^{3} \cdot 7 = 56

2^{3} \cdot 7

2^{3} = 8

= 8 \cdot 7

Multiply the numbers:

8 \cdot 7 = 56

= 56

= \frac{56}{5}

= \frac{56}{5}

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