Question

please help....

How many solutions does 3 cos2 x = 1 have on the interval [0, 2π)

Answer 1

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.

Answer 2

thank you.... :)