Study Notes
Trigonometric graphs visually represent the sine, cosine, and tangent functions over a range of angles. These graphs help solve trigonometric equations by finding all solutions between 0° and 360°.
- Sin Graph — a visual representation of the sine function. Example: The graph is continuous, repeats every 360º, and has a maximum value of 1 and a minimum value of -1.
- Cos Graph — a visual representation of the cosine function. Example: The graph repeats every 360º, does not pass through the origin, and has a maximum value of 1 and a minimum value of -1.
- Tan Graph — a visual representation of the tangent function. Example: The graph repeats every 180º, is not continuous, and has vertical asymptotes at 90º ± 180º.
Exam Tips
Key Definitions to Remember
- The sin graph is continuous and repeats every 360º.
- The cos graph repeats every 360º and does not pass through the origin.
- The tan graph repeats every 180º and has vertical asymptotes.
Common Confusions
- Confusing the period of the tan graph with that of the sin and cos graphs.
- Forgetting that the cos graph does not pass through the origin.
Typical Exam Questions
- What is the period of the sine graph? 360º
- Where are the vertical asymptotes on the tangent graph? At 90º ± 180º
- What is the maximum value of the cosine graph? 1
What Examiners Usually Test
- Understanding of the periodic nature of trigonometric graphs.
- Ability to identify key features like maximum and minimum values.
- Solving trigonometric equations using graphs.