Question

1. Sketch the curve,
y = 2 sinx for 0 < x < 2pi
2. By adding a suitable straight line to your sketch, determine the number of real roots of the
equation
2pi sin x = pi − x.
State the equation of the straight line.
I have done question 1 but I don't know how to do question 2 at all, any help would be appreciated.

Answer 1

Well, this is pretty much just drawing. The roots of the equation will basically be the intersection of the two graphs. So even though the places where the graph intersect may or may not be actual x-intercepts, they will be roots of the equation.

So Im sure you have 2sinx graphed. Well, 2pisinx is the same thing, except the maximum height is 2pi and the minimum height is -2pi. The other part, the pi - x part, is just a linear equation we can easily draw y = pi - x. When x is 0, y = pi, when y is 0, x = pi. SO I can just draw those two together now:



Should give you an idea : )