One Revolution Is 360 Degrees

Geometry Level 1

sin ⁡ 4 ∘ , sin ⁡ 4 0 ∘ , sin ⁡ 40 0 ∘ , sin ⁡ 400 0 ∘ , sin ⁡ 40000 0 ∘ \large \sin4^\circ, \quad \sin40^\circ, \quad \sin400^\circ, \quad \sin4000^\circ , \quad \sin400000^\circ

All of the above 5 numbers are equal in value except __________ \text{\_\_\_\_\_\_\_\_\_\_} .

sin ⁡ 4 ∘ \sin4^\circ sin ⁡ 4 0 ∘ \sin40^\circ sin ⁡ 40 0 ∘ \sin400^\circ sin ⁡ 400 0 ∘ \sin4000^\circ

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Chung Kevin by Chung Kevin , 45, Australia

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2 solutions

sin ⁡ ( θ ) = sin ⁡ ( 36 0 ∘ n + θ ) \sin(\theta)=\sin(360^{\circ}n+\theta) where n n is an integer.

Only sin ⁡ ( 4 ∘ ) \sin(4^{\circ}) is not expressible in that form for same value of θ \theta but the other four can.

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Thank you for your solution!

Chung Kevin - 5 years, 2 months ago

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My pleasure :)

A Former Brilliant Member - 5 years, 2 months ago

and im going to assume that theta in this case is 40

Karish Thangarajah - 5 years, 2 months ago

What if n=0 then it can be expressed anyway I am not satisfied with the solution

Roopinder Singh - 5 years, 2 months ago
Whitney Clark
Mar 26, 2016

It was easy, the period of sine is 360 deg, so the answer was most likely the only non-multiple of 10.

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