Question

I can’t figure out the next smallest non negative solution. Can you please help me?

Answer 1

Let w = cos(x)

The given equation turns into -5w^2 + 4w + 1 = 0. Use the quadratic formula to find that the two solutions, in terms of w, are:

• w = -1/5 = -0.2
• w = 1

The solution w = 1 leads to cos(x) = 1 which then becomes x = 0, x = 2pi, x = 4pi, etc. The general way to write this is x = 2pi*n where n is any integer. These angles are in radian mode.

The solution w = -0.2 leads to cos(x) = -0.2 which becomes x = arccos(-0.2) = 1.77215 approximately assuming your teacher wants the angle in radian mode. Unfortunately, I don't know the exact value of x here. There may not be an exact value, or finding this exact value may be well beyond the scope of this course.