Important Trigonometric Limits

Two Important Trigonometric Limits

In the app we investigate two very important trigonometric limits. These two limits are critical to finding derivative formulas for the sine and cosine functions. Both limits are taken as x approaches 0. For the function sin(x)/x we can display the limit process to see that we can sandwich theta between sin() and tan(). With some manipulation, we find that this gives us cos()<sin()/ < 1. Move the point B in the right window to manipulate the value of the red arclength, , which equals the x-value in the left window. As x = approaches 0, we see that the function values approach 1, by the Squeeze Theorem. We use this limit to obtain the other limit.