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

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cos^2(-30)

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

\frac{3}{4}

Decimal Notation

0.75

Solution steps

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

Rewrite using trig identities:

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

cos (- 3 0^{\circ})

Use the following property:

cos (- x) = cos (x)

cos (- 3 0^{\circ}) = cos (3 0^{\circ})

= cos (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}

= (\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}

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

cos^{2} (2 8^{\circ}) - sin^{2} (2 8^{\circ})

arccos (- 0.34)

arccos (- 0.75)

arccos (- 0.62)