What is the value of 1/2 cos^2(30) ?

The value of 1/2 cos^2(30) is 3/8

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1/2 cos^2(30)

\frac{1}{2} cos^{2} (3 0^{\circ})

\frac{3}{8}

Decimal Notation

0.375

Solution steps

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

Simplify

\frac{1}{2} (\frac{3}{2})^{2} : \frac{3}{8}

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

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

(\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}}

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 3 = 3

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

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

2 \cdot 2^{2}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

2 \cdot 2^{2} = 2^{1 + 2}

= 2^{1 + 2}

Add the numbers:

1 + 2 = 3

= 2^{3}

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

2^{3} = 8

= \frac{3}{8}

= \frac{3}{8}

- cos (0) + \frac{2 cos ^{3} ( 0 )}{3} - \frac{cos ^{5} ( 0 )}{5}

\frac{1 + tan ( 5 5 ^{\circ} ) tan ( 4 5 ^{\circ} )}{tan ( 5 5 ^{\circ} ) - tan ( 4 5 ^{\circ} )}

\frac{10}{tan ( 4 7 ^{\circ} )}

arccos (\frac{9}{13})

arctan (\frac{200}{175})