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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 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

catcode applet
This page uses Trigonometry applets from
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.

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 centre 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.

trigonometry

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

Full Glossary List

This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AP Calculus AB (USA)2TrigonometryTrig functions-
AP Calculus BC (USA)2TrigonometryTrig functions-
AQA A-Level (UK - Pre-2017)C2TrigonometryTrig functions-
AQA AS Maths 2017Pure MathsTrigonometrySin, Cos, Tan Graphs and Transformations-
AQA AS/A2 Maths 2017Pure MathsTrigonometrySin, Cos, Tan Graphs and Transformations-
CBSE X (India)TrigonometryIntroductionSurd form of sin, cos and tan 30,45 &60-
CCEA A-Level (NI)C2TrigonometryTrig functions-
CIE A-Level (UK)P1TrigonometryTrig functions-
Edexcel A-Level (UK - Pre-2017)C2TrigonometryTrig functions-
Edexcel AS Maths 2017Pure MathsTrigonometric RatiosSin, Cos, Tan Graphs and Transformations-
Edexcel AS/A2 Maths 2017Pure MathsTrigonometric RatiosSin, Cos, Tan Graphs and Transformations-
I.B. Higher Level3TrigonometryTrig functions-
I.B. Standard Level3TrigonometryTrig functions-
Methods (UK)M2TrigonometryTrig functions-
I.B. (MSSL)4TrigonometryTrig functions-
OCR A-Level (UK - Pre-2017)C2TrigonometryTrig functions-
OCR AS Maths 2017Pure MathsTrig Graphs and EquatiionsSin, Cos, Tan Graphs and Transformations-
OCR MEI AS Maths 2017Pure MathsTrig Graphs and EquationsSin, Cos, Tan Graphs and Transformations-
OCR-MEI A-Level (UK - Pre-2017)C2TrigonometryTrig functions-
Pre-Calculus (US)C4TrigonometryTrig functions-
Pre-U A-Level (UK)2TrigonometryTrig functions-
Scottish (Highers + Advanced)HM1TrigonometryTrig functions-
Scottish HighersM1TrigonometryTrig functions-
Universal (all site questions)TTrigonometryTrig functions-
WJEC A-Level (Wales)C2TrigonometryTrig functions-