Solve 12cosx-5sinx=4 for 0<x<90
You have to divide everything by sqrt(12 2+5 2) = 13
so
12/13 * cosx - 5/13 * sinx = 4/13
The reason that this is useful is that 5, 12, 13 is a pythagorean triad. (Draw the triangle, it will help you understand)
And I know that
sin(theta)cos(x) - cos(theta)sin(x) = sin(theta - x)
so
If sin(theta)=12/13, then cos(theta) has to equal 5/13 (put theta on your triangle and convince yourself that this is true)
also theta = sin -1(12/13) = 67.380 degrees
NOW
12/13 * cosx - 5/13 * sinx = 4/13
sin(67.380)*cosx - cos(67.380)*sinx = 4/13
sin (67.380 - x) = 4/13
sin -1(4/13) = 67.380 - x
17.920 = 67.380 - x
x = 67.380 - 17.920
x = 49.46 = 49 degrees (to the nearest degree.)
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