Solve for x, 5sin(x) - 3cos(x) = 2 , in the interval 0<x<2pi
5sin(x)-3cos(x)=2
Express in the form Rsin(x-@) = Rsin(x)cos@ - Rcos(x)sin@
Rcos@ =5
Rsin@ = 3
tan@ = 3/5 @=tan-1(3/5)= 0.540
R = sqrt(52 +32 )= sqrt(34)
sqrt(34)sin(x-0.540) = 2
sin(x - 0.540) = 0.343
Let Y = x-0.540
sinY = 0.343 in the interval -0.540 < Y < 5.743
Y = sin-1 (0.343)=0.350
Using CAST diagrams, we obtain 0.350 and pi-0.350 in this interval
Y = 0.350, 2.791
x = 0.350 + 0.540, 2.791 + 0.540
x = 0.890, 3.331
SM
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