Mathematics 133 -- Intensive Calculus for Science 1

Discussion 2 -- Log and Trig Functions

September 18, 2001

Background

The logarithm function g(x) = log_a(x) is by definition the inverse function of the exponential function f(x) = a^x. This means that

log_a(a^x) = x
and
a^log_a(x) = x
Last time we saw some of the properties of these functions and how they can be used to solve equations involving exponential terms. Today, we will continue that study. Then, we will also recall some properties of the trigonometric functions.

Discussion Questions

A) In class last time, we saw using properties of exponents that log_a(AB) = log_a(A) + log_a(B). Use the same ideas to explain why:
1. log_a(A/B) = log_a(A) - log_a(B)
2. log_a(A^p) = p log_a(A)
B) Using logarithms, find the solution(s) of the equations
1. 5 e^7x = 4
2. 2 e^x² = 2^2x
C) In high school, you have studied the trigonometric functions sin(x),cos(x),tan(x),sec(x),csc(x),cot(x). How do you find the values of these functions, if x is given as one of the acute angles in a right triangle? Without using a calculator, make a table of values for these functions and x = 0,30,45,60,90 (degrees).
D) Angles can be measured either in degrees or in radians. How is an angle of one radian defined? (If necessary, look this up in our text, and explain what you find in your own words.)

Assignment

One write-up per group of solutions for these problems, due Thursday, September 20.