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
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 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.
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) | 2 | Trigonometry | Trig functions | - |
| AP Calculus BC (USA) | 2 | Trigonometry | Trig functions | - |
| AQA A-Level (UK - Pre-2017) | C2 | Trigonometry | Trig functions | - |
| AQA AS Maths 2017 | Pure Maths | Trigonometry | Sin, Cos, Tan Graphs and Transformations | - |
| AQA AS/A2 Maths 2017 | Pure Maths | Trigonometry | Sin, Cos, Tan Graphs and Transformations | - |
| CBSE X (India) | Trigonometry | Introduction | Surd form of sin, cos and tan 30,45 &60 | - |
| CCEA A-Level (NI) | C2 | Trigonometry | Trig functions | - |
| CIE A-Level (UK) | P1 | Trigonometry | Trig functions | - |
| Edexcel A-Level (UK - Pre-2017) | C2 | Trigonometry | Trig functions | - |
| Edexcel AS Maths 2017 | Pure Maths | Trigonometric Ratios | Sin, Cos, Tan Graphs and Transformations | - |
| Edexcel AS/A2 Maths 2017 | Pure Maths | Trigonometric Ratios | Sin, Cos, Tan Graphs and Transformations | - |
| I.B. Higher Level | 3 | Trigonometry | Trig functions | - |
| I.B. Standard Level | 3 | Trigonometry | Trig functions | - |
| Methods (UK) | M2 | Trigonometry | Trig functions | - |
| I.B. (MSSL) | 4 | Trigonometry | Trig functions | - |
| OCR A-Level (UK - Pre-2017) | C2 | Trigonometry | Trig functions | - |
| OCR AS Maths 2017 | Pure Maths | Trig Graphs and Equatiions | Sin, Cos, Tan Graphs and Transformations | - |
| OCR MEI AS Maths 2017 | Pure Maths | Trig Graphs and Equations | Sin, Cos, Tan Graphs and Transformations | - |
| OCR-MEI A-Level (UK - Pre-2017) | C2 | Trigonometry | Trig functions | - |
| Pre-Calculus (US) | C4 | Trigonometry | Trig functions | - |
| Pre-U A-Level (UK) | 2 | Trigonometry | Trig functions | - |
| Scottish (Highers + Advanced) | HM1 | Trigonometry | Trig functions | - |
| Scottish Highers | M1 | Trigonometry | Trig functions | - |
| Universal (all site questions) | T | Trigonometry | Trig functions | - |
| WJEC A-Level (Wales) | C2 | Trigonometry | Trig functions | - |