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.