cos(theta) = .12 list six specific solutions

Question

^{need help solving for theta and also finding six solutions for the equation. k is the interger}

Answer 1

I'm guessing that you're studying inverse trigonometric functions now.  So let's use that in the solution.

 

Since cos θ = .12, the first solution is cos^-1 .12, or arccos .12.  On your calculator, you can find this to be 83.10° or 1.45 radians.  Let's use radians, but it doesn't really matter.

 

Now, the easiest way to find 5 other solutions is to remember that the period of the cos function is 2π.  So if you add 2π to 1.45, the cos will be the same, .12.  And if you add another 2π, it will be the same again.  Etc.

 

So you can create 6 solutions as follows:

 

1.45

1.45 + 2π

1.45 + 4π

1.45 + 6π

1.45 + 8π

1.45 + 10π

 

To make use of the integer k (which you stated in the problem but didn't say where it fit in), you can also write this as 1.45 + 2πk, where k goes from 0 to 5.