How to display the unit circle and corresponding trig graphs on a GDC (graphical display calculator). This explanation uses the TI-82/83/84 calculators.

1. Press MODE and select RADIAN, PAR, SIMUL.

2. Press Y= and enter X1T=cos(T), Y1T=sin(T), X2T=T, Y2T=sin(T).

3. Press WINDOW and set Tmin=0, Tmax=6.28,Tstep=0.1, Xmin=-2, Xmax=7.4, Xscl=1.57,Ymin=-3.1, Ymax=3.1, Yscl=1

4. Press GRAPH

The unit circle and the graph of y=sin x will be displayed simultaneously. Use your GDC to do the same for cos x and tan x.

Click

1. Press MODE and select RADIAN, PAR, SIMUL.

2. Press Y= and enter X1T=cos(T), Y1T=sin(T), X2T=T, Y2T=sin(T).

3. Press WINDOW and set Tmin=0, Tmax=6.28,Tstep=0.1, Xmin=-2, Xmax=7.4, Xscl=1.57,Ymin=-3.1, Ymax=3.1, Yscl=1

4. Press GRAPH

The unit circle and the graph of y=sin x will be displayed simultaneously. Use your GDC to do the same for cos x and tan x.

Click

**Start**to see the graph of the sine function being drawn from the unit circle definition. The*cosine wave*can be produced in the same way. The*tangent wave*has very different characteristics.## Software/Applets used on this page

This page uses Trigonometry applets from

catcode.com

catcode.com

## Glossary

### circle

a conic curve with equation (x-a)²+(y-b)²=r²

### cosine

The trigonometrical function defined as adjacent/hypotenuse in a right-angled triangle.

### function

A rule that connects one value in one set with one and only one value in another set.

### gdc

graphic display calculator

### graph

A diagram showing a relationship between two variables.

The diagram shows a vertical y axis and a horizontal x axis.

The diagram shows a vertical y axis and a horizontal x axis.

### mode

the value in a set of discrete data that occurs most frequently

### radian

a measure of angle equal to the size of the angle subtended at the center of a circle of radius r by an arc of length r.

### sine

The trigonometrical function defined as opposite/hypotenuse in a right-angled triangle.

### tangent

1. The trigonometrical function defined as opposite/adjacent in a right-angled triangle.

2. A straight line that touches a curve at one point.

2. A straight line that touches a curve at one point.

### trigonometry

The study of the relationships between the angles and sides of triangles.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AP Calculus AB (USA) | 1 | Graphic calculators | Graph sketching | - |

AP Calculus BC (USA) | 1 | Graphic calculators | Graph sketching | - |

Universal (all site questions) | G | Graphic calculators | Graph sketching | - |