4 sin(2y-0.3)+5 cos(2y-0.3)=0

Question

Please solve in terms of rad

Answer 1

4sine(x) + 5kosine(x)=0

4 sine=-5kosine

sine(x)=(-5/4)kosine(x)

sine^2 =(25/16) kosine^2=1.5625 kosine^2

sine^2=1.5625*[1-sine^2(x)]

sine^2(1+1.5625)=1.5625

2.5625 sine^2=1.5625

sine^2(x)=(1.5625/2.5625)=0.609756097

sine(x)=root(0.609....)=0.780868809

invers sine giv x=51.34019175 deg

2y-0.3=51.34019175

2y=51.34...+0.3=51.64019175

y=51.640.../2=25.82009587