Find the exact value of cos160/sin70.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to remember that `sin alpha =cos (90^o - alpha), ` hence substituting `160^o`  for alpha yields:

`cos 160^o = sin (90^o - 160^o)`

`cos 160^o = sin (-70^o)`

You need to remember that sine function is odd, hence `sin (-70^o) = -sin (70^o)`

Hence, substituting `-sin (70^o)`  for cos `160^o`  yields:

`cos 160^o/ sin 70^o = -sin (70^o)/sin (70^o) = -1`

Hence, evaluating the exact value of fraction `cos 160^o/ sin 70^o`  yields`-1.`

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