INSTRUCTORS Raffi Hovasapian John Zhu

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• ## Related Books

 0 answersPost by Arjun Chaturvedi on April 16, 2014Please provide more details and examples in the lectures that you give. 2 answersLast reply by: Akbar RizviMon Jun 9, 2014 2:46 PMPost by Nada Al Bedwawi on January 12, 2014Hi Prof.What do you mean by A=max - min/2 ? What does the "A"(capital) stand for?

### Trigonometric Functions

• a:changes amplitude
• b:changed period
• c:shifts horizontally
• d:shifts vertically

### Trigonometric Functions

Simplify tanx cscx
• y = tanx cscx
• = [sinx/cosx] [1/sinx]
= [1/cosx] = secx
Simplify cscx cosx
• y = cscx cosx
• = [1/sinx] cosx
• = [cosx/sinx]
=cotx
Simplify [4x sinx/(x2 cos3x)]
• y = [4x sinx/(x2 cos3x)]
• = [4x/(x2)] [sinx/cos3x]
and cannot be combined because their arguments differ. The arguments must be the same to rewrite trig functions. 0Find the domain and range of
• sin and cos are periodic functions, meaning the outputs will repeat once the input is shifted over a full period. The unit circle is a good way to see this. No matter what real numbers we put into the function, the same pattern repeats. The output never exceeds 1 or goes below -1
Domain (), Range [-1, 1] 0Find the domain and range of
This is similar to the previous problem, but it's a bit trickier because it introduces zero into the denominator. The function is said to be undefined where the input results in a zero in the denominator. For this function, we won't have any problems when the denominator is not zero. So the domain involves any x when is not zero. is zero at any multiple of , including zero. Now, we're dividing by really tiny numbers (approaching zero). An integer divided by a very small number, is a very large number. Domain is all real numbers, but cannot equal any multiple of . where n is any integer. Range 0Graph
• This is very similar to the regular cos graph, except that its period is changed, or quished." Its usual period of is now .
0Graph
This is similar to the regular sin graph, but it is shifted UP by one unit. 0Graph
• is very different from . Radians are used unless otherwise specified. By convention, the variable typically implies use of degrees).
• has a period of , meaning that going units in x in either direction will return the same result
• etc...
• so this is the same graph as
0Graph
• The number out front here determines the amplitude. In this case, it's 3. So from minimum to maximum, this graph will cover 6 units total. Multiplying the x here by 2 changes the period from to .
0Graph
• The positive 4 there moves the graph over 4 units to the left. The -1 in that location means the graph is shifted down 1. This is the same graph as the previous problem, but shifted down 1 and 4 to the left.

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.