What is cos (7pie/4)=?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You may express the angle `(7pi)/4` as the following difference:

`(7pi)/4 = (8pi - pi)/4`

Splitting the difference yields:

`(7pi)/4 = (8pi)/4 - pi/4`

`(7pi)/4= 2pi - pi/4`

Taking the cosine function, yields:

`cos ((7pi)/4) = cos (2pi - pi/4)`

Since `2pi - pi/4` represents the reference angle for `(7pi)/4` , in quadrant 4, yields:

`cos (2pi - pi/4) = cos (pi/4) = sqrt2/2`

Hence, evaluating the value of `cos ((7pi)/4)` , using the reference angle `2pi - pi/4` , yields `cos ((7pi)/4) = cos (pi/4) = sqrt2/2.`

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