A little help with my statics homework

[MEstudent]

So I am doing a homework problem for my statics class and we are trying to solve for the magnitude of a force and two angles. So far I have done everything right. I have broke everything down into components and did a mixed triple product to get submations in the x, y, and z axis. I was able to solve for teh magnitude of the force and one angle, but i cant figure out how to get the last angle with the equation i have. Here is the equasion:

41.43sin(x)-7.21cos(x)=26

Because it involves sine and cosine and the x value is the same i figured i should put it in to terms of tan(x) and then solve for angle x, but I cant figure out how to do it. The answer is given in the back of the book and is 48.1 degrees. If anyone can give me some help i would really appreciate it. Thanks.

 

[o_O]

Put one of the trig functions into terms of the other using the identity: \(\displaystyle sin^{2}x + cos^{2}x = 1\)

\(\displaystyle 41.43sin(x)-7.21cos(x)=26\)

\(\displaystyle 41.43sinx - 7.21\sqrt{1 - sin^{2}x} = 26\)

\(\displaystyle 41.43sinx - 26 = 7.21\sqrt{1 - sin^{2}x} \quad \mbox{Square both sides ... }\)