SOLUTION: Verify the reduction formula: a) sin(x - 5pi/2)= -cosx b) sin(x+ pi)= -sinx

Question 535678: Verify the reduction formula:
a) sin(x - 5pi/2)= -cosx
b) sin(x+ pi)= -sinx
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Verify the reduction formula:
a) sin(x - 5pi/2)= -cosx
use sin addition formula
sin(s-t)=sin s cos t-cos s sin t
sin(x-5π/2)=sinxcos5π/2-sin5π/2cosx
reference angle for 5π/2=π/2
cos(5π/2)=cos(π/2)=0
sin(5π/2)=sin(π/2)=1
sin(x-5π/2)=sinxcos5π/2-sin5π/2cosx
sin(x-5π/2)=0-cosx=-cosx
..
b) sin(x+ pi)= -sinx
sin(s+t)=sin s cos t+cos s sin t
sin(x+π)=sinxcosπ+cosxsinπ
cos(π)=-1
sin(π)=0
sin(x+π)=sinx*(-1)+cosx*0
sin(x+π)=-sinx
verified: left side=right side
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