Solve for x (show steps taken for best and first rating): 24sin(x) - 12cos(x) = 5

Donna Flynn 2022-07-26 Answered
Solve for x (show steps taken for best and first rating):
24sin(x) - 12cos(x) = 5
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Answers (1)

thenurssoullu
Answered 2022-07-27 Author has 13 answers
The key point is sin^2 x + cos^2 x = 1. So you need to remove the cos (or the sin, doesn't matter), rearrange, and solve the quadratic equation:
24sinx-12cox = 5
=> -12cosx = 5 - 24 sinx
=> -12 sqrt(1 - sin^2 x) = 5 - 24 sinx
=> 144 (1 - sin^2 x) = (5 - 24 sinx)^2
... Now in this last step I have squablack both sides. Note this will also solve the equation where there is a +12 instread of a -12, so you will get extra solutions which you will need to discard.

Anyway, you then rearrange it into a quadratic equation, which you then solve for sinx. This will give two possible values of sinx, i.e. four possible values of x (between 0 and 360 degrees). Then you need to check each of those 4 values of x: two will work, two won't.
x1=37.3, and x2 = 15.8

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