How do you simplify #sin (cos^-1 (-1/4))#?

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Answer 1 · 2018-05-06T05:59:02

The answer is #=+-sqrt15/4#

Let #x=cos^-1(1/4)#

Then,

#cosx=1/4#

Therefore,

#sin(cos^-1(1/4))=sinx#

#sin^2x+cos^2x=1#

#sinx=+-sqrt(1-cos^2x)#

#=+-sqrt(1-1/16)#

#=+-sqrt15/4#