Question

Find all solutions to the equation in the interval [0,2pi): sin(x+pi)-sin(x)-1=0

Answer 1

sin(x+pi)-sinx+1=0
sinx cos pi + cosx sin pi - sinx +1 =0
-sinx-sinx+1=0
-2sinx=-1
sinx=1/2
x=pi/6+2npi
or x=5pi/6+2npi
P.S ,cos pi =-1 ,and sin pi =0

cos(x+pi)-cosx-1=0
cosx cos pi -sinx sin pi - cosx-1=0
-cosx-cosx-1=0
-2cosx=1
cosx=-1/2
x=-pi/3+npi

sin(x+pi/6)-sin(x-pi/6)=1/2
sinx sin pi/6 + cosx cos pi/6 - (sinx sin pi/6 - cosx cos pi/6)=1/2
sinx sin pi/6 + sqrt3 /2 cosx - sinx sin pi/6 + sqrt3 /2 cosx =1/2
sqrt3cosx=1
cosx=1/2sqrt3
x=73 degrees
hope this helps :)

Answer 2

thank you!!