What is the value of 122/2 cos^2(30)*cos^2(60) ?

The value of 122/2 cos^2(30)*cos^2(60) is 183/16

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122/2 cos^2(30)*cos^2(60)

\frac{122}{2} cos^{2} (3 0^{\circ}) \cdot cos^{2} (6 0^{\circ})

\frac{183}{16}

Decimal Notation

11.4375

Solution steps

\frac{122}{2} cos^{2} (3 0^{\circ}) cos^{2} (6 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}

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{122}{2} (\frac{3}{2})^{2} (\frac{1}{2})^{2}

Simplify

\frac{122}{2} (\frac{3}{2})^{2} (\frac{1}{2})^{2} : \frac{183}{16}

\frac{122}{2} (\frac{3}{2})^{2} (\frac{1}{2})^{2}

Apply exponent rule:

a^{m} b^{m} = (ab)^{m}

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

= \frac{122}{2} (\frac{1}{2} \cdot \frac{3}{2})^{2}

\frac{3}{2} \cdot \frac{1}{2} = \frac{3}{4}

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

Multiply fractions:

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

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

Multiply:

3 \cdot 1 = 3

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{3}{4}

= \frac{122}{2} (\frac{3}{4})^{2}

Divide the numbers:

\frac{122}{2} = 61

= 61 (\frac{3}{4})^{2}

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

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

Apply exponent rule:

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

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

= 61 \cdot \frac{3}{4 ^{2}}

Multiply fractions:

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

= \frac{3 \cdot 61}{4 ^{2}}

Multiply the numbers:

3 \cdot 61 = 183

= \frac{183}{4 ^{2}}

4^{2} = 16

= \frac{183}{16}

= \frac{183}{16}

cos (π) (0.534716) - ln (0.534716)

\frac{20}{sin ( 14.8 8 ^{\circ} )}

\frac{1}{sec ( 3 0 ^{\circ} )}

arctan (\frac{4.99}{9.807} + 0.4)

cos (\frac{0.577}{53.2})

What is the value of 122/2 cos^2(30)*cos^2(60) ?
The value of 122/2 cos^2(30)*cos^2(60) is 183/16