Question

This is a question that involves graphing although I'm not very good at it especially Trigonometric Functions >_<

a) Find the equation of the tangent to the curve y = sinx at the origin

For part (a) I've already found the equation its: y = 0

b) Using a graph or otherwise, state the number of solutions to the equation sinx = x

c) Let m (tangent) be a positive number. For what set of values does the equation sinx = mx have exactly 3 solutions satisfying -π ≤ x ≤ π

Answer 1

If y = sin x
then the slope is cos x
which is one at the origin or 45 degrees or
y = x is the equation of the tangent to y = sin x at the origin.

sin x is >/=-1 and </= +1
so this whole thing will only work between x = -1 and x = +1
Now in part a we decided that y = x hit the y = sin x curve at the origin. Does it hit anywhere else? No, look at your graph.

Again look at your graph.
If m is greater than one, the y = mx hits y = sin x only at the origin
For m = 0, it hits at x = -pi, 0, and pi
for x >0 and less than 1, it hits in the first quadrant, at zero and in the third quadrant
so
0<m<1