MAT 1339 Chapter 4-5: chapter4n5.pdf

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1339
• Professor: Maryam Hosseini

Document Summary

To know the derivatives of the trigonometric functions and be able to use them in applications. To know the derivatives of exponential functions. To understand the properties of the exponential function f (x) = ex. To understand the properties of the natural logarithm function f (x) = ln x. To be able solve application problems involving exponentials. In calculus, we always use radian measure for angles the formulas we will nd below for the derivatives of the trigonometric functions require radian measure to be true. Recall the de nitions of the trigonometric functions from a right-angled triangle. cos = sin = tan = sec = csc = cot = adjacent hypotenuse opposite hypotenuse opposite adjacent cos . 1 hypotenuse adjacent hypotenuse opposite cos sin adjacent opposite hypotenuseoppositeadjacentthetaor, from the unit circle, x2 + y2 = 1. 2 x = cos and y = sin . All of the functions are periodic, ie they repeat themselves over and over again.