MAT 106 040 TRIGONOMETRY
LECTURE 13
WING HONG TONY WONG
8.1 Angles, arcs and their measures
A line AB passes through two points A and B and never ends, a segment AB terminates at
A and B , and a ray AB terminates at A but never ends on the other end.
Give
MA 106 040 TRIGONOMETRY
LECTURE 1
WING HONG TONY WONG
Inverse functions
This lecture is related to Section 5.1.
A function is a number machine: for each input of a real number, there will be a output
of a real number. Sometimes, when we are given the outp
MA 106 040 TRIGONOMETRY
LECTURE 6
WING HONG TONY WONG
5.3 Logarithms and their properties
Recall from the last lecture that we gave the denitions of the logarithmic function base a.
In short, it is the inverse function of the exponential function, and one
MA 106 040 TRIGONOMETRY
LECTURE 5
WING HONG TONY WONG
5.3 Logarithms and their properties
Recall from the last lecture that the graphs of exponential functions f (x) = ax , where a
is positive and not equal to 1, are either strictly increasing or strictly
MA 106 040 TRIGONOMETRY
LECTURE 4
WING HONG TONY WONG
5.2 Compound interest, continuous compounding and e
In the last lecture, we made some conclusive remarks concerning inverse functions, and
discussed about exponential functions and their graphs.
Let P
MA 106 040 TRIGONOMETRY
LECTURE 2
WING HONG TONY WONG
Inverse functions
This lecture is related to Section 5.1 and 5.2.
Let f : X Y be a function. By nding an inverse to this function, we mean that for
each output of the function, we look for what input c
MA 106 040 TRIGONOMETRY
LECTURE 3
WING HONG TONY WONG
5.1 Conclusions for inverse functions
In short, inverse function f 1 is the function which undoes the original function f . For
example, f (x) = x + 2 and g (x) = x 2 undo each other, so g = f 1 ; f (x
MA 106 040 TRIGONOMETRY
LECTURE 7
WING HONG TONY WONG
Last lecture, we have learnt how to evaluate and simply expressions involving logarithms.
5.4 Logarithmic Functions
Once again,
for all a > 0 and a = 1, loga ax = x, and
for all x > 0, a > 0 and a = 1,
MA 106 040 TRIGONOMETRY
LECTURE 8
WING HONG TONY WONG
Last lecture, we introduced logarithm functions. For example, we discussed the domain,
the range and the graphs of logarithmic functions f (x) = loga x for both 0 < a < 1 and a > 1.
5.4 Logarithmic Fun
MAT 106 040 TRIGONOMETRY
LECTURE 18
WING HONG TONY WONG
Last lecture, we nished the discussions on radian measures and various related formula,
including the length of an arc, area of a sector, angular speed and linear speed.
8.6 Denition of trigonometric
MAT 106 040 TRIGONOMETRY
LECTURE 19
WING HONG TONY WONG
Last lecture, we dened trigonometric functions using right-angled triangles.
8.6 Denition of trigonometric functions using right-angled triangles
The following are the cofunction identities.
sin A =
MAT 106 040 TRIGONOMETRY
LECTURE 17
WING HONG TONY WONG
Last week, we discussed about positive angles, negative angles and coterminal angles. We
also talk about degrees, minutes and seconds, as well as radian measures of an angle.
8.1 Angles, arcs and the
MA 106 040 TRIGONOMETRY
LECTURE 11
WING HONG TONY WONG
5.5 Exponential and logarithmic equations and inequalities
Example 1. (5.5.3) Solve 3e2x + 1 = 5.
Example 2. (5.5.15) Solve 4x1 = 32x .
Example 3. (5.5.25) Solve 0.05(1.15)x = 5.
Example 4. (5.5.43) S
MA 106 040 TRIGONOMETRY
LECTURE 9
WING HONG TONY WONG
Last lecture, we discussed how to nd the domain and range of logarithmic functions
like f (x) = log6 (2x2 7x 8), and how to sketch the graph of logarithmic functions like
f (x) = log3 (9x + 2).
5.4 Log
MA 106 040 TRIGONOMETRY
LECTURE 10
WING HONG TONY WONG
5.4 Logarithmic Functions
Example 1. Sketch the graph f (x) = | log3 (x 5)| and f (x) = log3 |x 5|.
Example 2. Find the inverse function of f (x) = 2x + 3. What is the range of f (x)?
The inverse func