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Popular >

cos^4(45)

Solution

cos^{4} (4 5^{\circ})

Solution

\frac{1}{4}

+1

Decimal Notation

0.25

Solution steps

cos^{4} (4 5^{\circ})

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\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{2}{2}

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

Simplify

(\frac{2}{2})^{4} : \frac{1}{4}

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

Apply exponent rule:

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

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

(2)^{4} : 2^{2}

Apply radical rule:

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

= (2^{\frac{1}{2}})^{4}

Apply exponent rule:

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

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

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

\frac{1}{2} \cdot 4

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 4 = 4

= \frac{4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2

= 2^{2}

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

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{2}}{2 ^{4}} = \frac{1}{2 ^{4 - 2}}

= \frac{1}{2 ^{4 - 2}}

Subtract the numbers:

4 - 2 = 2

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

2^{2} = 4

= \frac{1}{4}

= \frac{1}{4}

Popular Examples

cos(pi/4)-pi/4 sin(pi/4)

cos (\frac{π}{4}) - \frac{π}{4} sin (\frac{π}{4})

0.832*10^9*cos^2(33.69)*sin^2(33.69)

0.832 \cdot 1 0^{9} \cdot cos^{2} (33.6 9^{\circ}) \cdot sin^{2} (33.6 9^{\circ})

sec^{2} (- 2)

sin (- 4 + i)

arccot(200/83+cot(15))

arccot (\frac{200}{83} + cot (1 5^{\circ}))

Frequently Asked Questions (FAQ)

What is the value of cos^4(45) ?
The value of cos^4(45) is 1/4