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Popular >

cos^3(180)

Solution

cos^{3} (18 0^{\circ})

Solution

- 1

Solution steps

cos^{3} (18 0^{\circ})

Use the following trivial identity:

cos (18 0^{\circ}) = (- 1)

cos (18 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}

= (- 1)

= (- 1)^{3}

Simplify

(- 1)^{3} : - 1

(- 1)^{3}

Apply exponent rule:

(- a)^{n} = - a^{n},

if

n

is odd

(- 1)^{3} = - 1^{3}

= - 1^{3}

Apply rule

1^{a} = 1

= - 1

= - 1

Popular Examples

\frac{8}{sin ( 3 5 ^{\circ} )}

sec (7 1^{\circ}) (3 0^{\circ})

9.8 cos (7 5^{\circ})

1 + cos (3 0^{\circ})

2cos^2((3pi)/5)-1

2 cos^{2} (\frac{3 π}{5}) - 1

Frequently Asked Questions (FAQ)

What is the value of cos^3(180) ?
The value of cos^3(180) is -1