anonymous 5 years ago please help.... How many solutions does 3 cos2 x = 1 have on the interval [0, 2π)

1. anonymous

it has two solutions, one in the first quadrant, and one in the fourth quadrant. This can be solved algebraically and with the inverse cosine function. If this equation is $3\cos (2x)=1$ I would sub $2\cos ^2(x)-1$ for cos(2x). This will make it easier to solve. It is which angles x or theta for which the cosine equals whatever number you pull out algebraically. Because cosine is positive again for the angles between (3/2)pi and 2pi, There will be a second solution angle. (360 degrees - whatever angle you find using cos^(-1). I don't have a calculatorwith me otherwise I'd give them to you and writing the steps with equation inserter takes too long. For $3\cos ^2(x)=1$$\cos^{-1} (x)=\sqrt{1/3}$ is your first angle, then subtract from 360 or 2pi to get your other one.

2. anonymous

thank you.... :)