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Geometry Level 1

∏ k = 1 179 cos ⁡ ( k ° ) = ? \Large \prod _{ k=1 }^{ 179 }{ \cos { \left( k° \right) } }=?


The answer is 0.

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Shivamani Patil by shivamani patil , 21, India

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4 solutions

Shivamani Patil
Jul 7, 2015

Notice cos ⁡ 90 ° = 0 ∴ ∏ k = 1 179 cos ⁡ ( k ° ) = 0 \cos { 90° } =0\therefore \prod _{ k=1 }^{ 179 }{ \cos { \left( k° \right) } =0 } .

8 Helpful 0 Interesting 0 Brilliant 0 Confused

the given expression equals to 》 cos1•cos2.........cos178•cos179 after Organising we get》 (cos1 •cos179) (cos2 •cos178).......cos90 but here we noticed that cos 90=0 which makes the whole expression equals to 0.

aash raj - 5 years, 11 months ago
Akshay Yadav
Jul 8, 2015

The following function means -

cos1 x cos2 x ...x cos 178 x cos179

But we notice,

cos1 x cos2 x ...x cos 90 x cos91 x ...x cos179

We know cos 90 = 0,

Hence,

The whole multiplication results to 0.

4 Helpful 0 Interesting 0 Brilliant 0 Confused
Hitoshi Yamamoto
Oct 6, 2015

Como o "cos(90°) = 0", então o produtório é igual a zero.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Pooja Rao
Jul 9, 2015

since cos90 = 0 this implies the whole multiplication is = 0

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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