* Graphing Calculator activities with Trigonometric Functions *  Exercise 2 *

Trigonometric Functions vary from rolling hills to long curved lines and U shaped curves.

The Unit Circle is a basic concept with Trigonometry since Trigonometric graphs are points

on a Unit Circle as a right triangle, which starts in Quadrant I and revolves around to Quadrant IV.

There are six basic Trigonometric Functions two can be defined easily from The Unit Circle.

They are Sin and Cos while the Tan Function is defined as the ratio of Sin/Cos.

The remaining three are definded as reciprocals of the first three and easily expressed.

They are: Csc = 1/Sin Sec = 1/Cos Cot = 1/Tan See about reciprocals.

The basic equation of all Trigonometric Functions is: y = AsinBx+C

A is amplitude or height B is frequency or periodic cycle C is a shift from origin

A review of basic Trigonometric Functions.   Ok, let's try exercises with Csc!

Remember all you have to do is type an GC Mode equation in then press enter.

Remember to use  *  for multiply and /  for divide and ^   for exponents.

Here are examples to try.  Maybe, print out this page before selecting a Graphing Calculator.

It is important to predict what you would expect the graph to appear as before Graphing?

It is also important to only change one variable at a time A or B or C!

What happens when the amplitude A is varied?    Direction?

What happens if A is Negative? Compare direction to (+)?

Math Mode:  y = +2cscx        GC Mode: +2csc(x)

Math Mode:  y = +4cscx        GC Mode: +4csc(x)

Math Mode:  y = +6cscx         GC Mode: +6csc(x)

Changing B varies the frequency of the Csc graph. Does it?

What happens when the frequency B becomes smaller?

Math Mode:  y = +csc2x         GC Mode:  csc(2*x)

Math Mode:  y = +csc4x        GC Mode: csc(4*x)

Math Mode:  y = +csc6x         GC Mode:  csc(6*x)

What happens when Csc is shifted by varing C ?

Use: +p/2 +p +3p/2 +2p How about (-C) ?

Math Mode:  y = +csc(x+p/2)         GC Mode: +csc(x+pi/2)

Math Mode:  y = +csc(x+p)        GC Mode: +csc(x+pi)

Math Mode:  y = +csc(x+3p/2)         GC Mode: +csc(x+3*pi/2)

Try and predict what the Graph with A,B,C changed?

Try and sketch it on a piece of paper using a coordinate system!

Math Mode:  y = -2csc(x-p)         GC Mode: -2*csc(x-p) 

Math Mode:  y = +1/2csc(x+p/2)       GC Mode: +1/2*csc(x+p/2)      

Math Mode:  y = -4csc(x-2p)   GC Mode:  -4*csc(x-2p)

Now try the same exercises using SEC and COT…

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Click on one of the Online Calculators:  I like the first one but they are all great!

GCalc!  The equation box is at the top of the screen.

Oh yel, you have to press the Click to Start GCalc button.

Click the Reset Button (Top Right) and Yes to clear screen.

CoolMath Graphing Calculator   The equation box is at the top of the screen.

Click the Cls button at the bottom right of commands to clear screen.

GraphIt!   The equation box is at the bottom of the screen.

Oh yel, you have to press the  Plot It!  at bottom left of screen.

Also, click the check mark in front of grid before starting to show grid.

Also, typing in a new Linear Function automatically clears the screen.

Tom Love               Malone College          Fall 2003

y = Csc(x)

+p/2

+2p

+3p/2

-p/2

-3p/2

-2p

-2p -3p/2 -p -p/2 +p/2 +p +3p/2 +2p