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

Donna Flynn

Donna Flynn

Answered question

2022-07-26

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

Answer & Explanation

thenurssoullu

thenurssoullu

Beginner2022-07-27Added 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

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?