SOLUTION: If cosx = -2/5, and (pi/2) < x < pi, find the exact value of sin(x-(pi/4))? The answer I got is ((-sqrt 21)+2)/ 5 sqrt2) I don't know if that is right though. Thank you f

Question 928208: If cosx = -2/5, and (pi/2) < x < pi, find the exact value of sin(x-(pi/4))?
The answer I got is ((-sqrt 21)+2)/ 5 sqrt2)
I don't know if that is right though.
Thank you for the help!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
If cosx = -2/5, and (pi/2) < x < pi, find the exact value of sin(x-(pi/4))?
sinx=√(1-cos^2(x))=√(1-4/25)=√(21/25)=√21/5
sin(x-π/4)=sinx*cos(π/4)-cos(x)*sin(π/4)=√21/5*√2/2-(-2/5)*√2/2
=√42/10+2√2/10=(√42+2√2)/10
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