Trigonometric Graphs (Sine, Cosine & Tangent) - SS3 Mathematics Lesson Note
SINE GRAPH
Given the following values of \(x\),
|
\[\mathbf{x}\] |
\[0{^\circ}\] |
\[30{^\circ}\] |
\[60{^\circ}\] |
\[90{^\circ}\] |
\[120{^\circ}\] |
\[150{^\circ}\] |
\[180{^\circ}\] |
\[210{^\circ}\] |
\[240{^\circ}\] |
\[270{^\circ}\] |
\[300{^\circ}\] |
\[330{^\circ}\] |
\[360{^\circ}\]
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
\[\mathbf{\sin}\mathbf{x}\] |
\[0\] |
\[0.5\] |
\[0.87\] |
\[1\] |
\[0.87\] |
\[0.5\] |
\[0\] |
\[- 0.5\] |
\[- 0.87\] |
\[- 1\] |
\[- 0.87\] |
\[- 0.5\] |
\[0\] |
The following sine graph is obtained,
COSINE GRAPH
Given the following values of \(x\),
|
\[\mathbf{x}\] |
\[0{^\circ}\] |
\[30{^\circ}\] |
\[60{^\circ}\] |
\[90{^\circ}\] |
\[120{^\circ}\] |
\[150{^\circ}\] |
\[180{^\circ}\] |
\[210{^\circ}\] |
\[240{^\circ}\] |
\[270{^\circ}\] |
\[300{^\circ}\] |
\[330{^\circ}\] |
\[360{^\circ}\]
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
\[\mathbf{cos\ }\mathbf{x}\] |
\[1\] |
\[0.87\] |
\[0.5\] |
\[0\] |
\[- 0.5\] |
\[- 0.87\] |
\[- 1\] |
\[- 0.87\] |
\[- 0.5\] |
\[0\] |
\[0.5\] |
\[0.87\] |
\[1\] |
The following sine graph is obtained,
TANGENT GRAPH
Given the following values of \(x\),
|
\[\mathbf{x}\] |
\[0{^\circ}\] |
\[30{^\circ}\] |
\[60{^\circ}\] |
\[90{^\circ}\] |
\[120{^\circ}\] |
\[150{^\circ}\] |
\[180{^\circ}\] |
\[210{^\circ}\] |
\[240{^\circ}\] |
\[270{^\circ}\] |
\[300{^\circ}\] |
\[330{^\circ}\] |
\[360{^\circ}\]
|
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
\[\mathbf{tan\ }\mathbf{x}\] |
\[0\] |
\[0.58\] |
\[1.73\] |
\[\infty\] |
\[- 1.73\] |
\[- 0.58\] |
\[0\] |
\[0.58\] |
\[1.73\] |
\[\infty\] |
\[- 1.73\] |
\[- 0.58\] |
\[0\] |
The following tangent graph is obtained,
Points such as where \(x = 90{^\circ}\) or \(270{^\circ}\) then \(\tan x\ \rightarrow \ \infty\) are known as asymptotes and \(\tan x\) is undefined at these points.