Question

How many solutions does sin(x) = 0.01 have in the interval [0, 2π)?

Answer 1

think of a unit circle. how many times, if we go around it one time( [0,2pi) ), will its "height" be equal to .01?

Answer 2

Does putting in sin(.01) in a calculator work?

Answer 3

Ah

Answer 4

no we want sin(theta) = .01 but you cant get this from a calc because they limit the domain of inverse...

Answer 5

*they force it to be a function.

Answer 6

ok so if we start at 3 o'clock and go all the way around how many times will we be at that .01 mark?

Answer 7

The limit is until it reaches 2pi, right?

Answer 8

um, no limit. but 2pi says we go around once.

Answer 9

Only once?

Answer 10

on the pic I drew, i put two points where if we went around the circle once we would be at .01

Answer 11

Oh....

Answer 12

I think I understand

Answer 13

Is there a simple way to find it when it is not directly on the unit circle?