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What is cos1deg*cos2deg*cos3deg*------*cos103deg?

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lemong | Student, Undergraduate | Honors

Posted July 4, 2012 at 7:32 AM via web

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What is cos1deg*cos2deg*cos3deg*------*cos103deg?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted July 4, 2012 at 8:39 AM (Answer #1)

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Since you should evaluate a product, you need to identify if there is a factor that equals zero, such that the product cancels.

You need to remember that `cos 90^o = cos 270^o = 0` .

Notice that one of factors of the given product is `cos 90^o` , hence, the product cancels such that:

`cos 1^o*cos 2^o*cos 3^o*.....*cos 90^o*...*cos 103^o`

`cos 1^o*cos 2^o*cos 3^o*.....*0*...*cos 103^o = 0`

Hence, evaluating the given product yields `cos 1^o*cos 2^o*cos 3^o*.....*cos 90^o*...*cos 103^o = 0` .

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