Answer:
sinθ ≈ θ for small angles of θ ( less than 14 degrees will give an error of less than 1%)
Step-by-step explanation:
several ways to prove this. The easiest way is graphically.
let θ = x, and we are to prove sin x ≈ x
plot y = sin x and y = x on the same curve (see attached)
by observation we can see that the red line (y = x) coincides with the blue line (y = sin x) at values very close to x =0, meaning that as you get closer to zero, y=sin x will be closer and closer to y=x
typically to get the values of y=sin x within 1% of y = x, the value of x is less than 0.2 radians (or about 14 degrees)
