Cos(3x+28°)=sin(2x+48°)
in Other Math Topics by Level 4 User (6.9k points)

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We can write this: sin(90-(3x+28))=sin(2x+28).

So 90-3x-28=2x+28, 34=5x, x=6.8° is one solution.

But cos(3x+28)=cos(-3x-28)=sin(90+3x+28)=sin(2x+28), 90+3x=2x, x=-90°=270° is another solution.

And there are many solutions derived from these two, because cos(360+A)=cosA and sin(360+A)=sinA.

The easiest way to find all the solutions is to draw a graph of y=cos(3x+28) and y=sin(2x+28). You will see where the two curves intersect and you should spot a pattern that will enable you to write a general expression for all the solutions (e.g., 6.8, 78.8, 150.8, 222.8, 270, 294.8, 366.8, etc.).

Two general formulae for x in degrees are:

x=6.8+72n (derived from 5x=34+360n) and x=270+360n, where n is any integer, positive or negative.

by Top Rated User (645k points)

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