Study Notes
The unit circle is a fundamental concept in trigonometry, representing a circle with a radius of one unit centered at the origin. It is used to define the sine, cosine, and tangent functions based on the coordinates of points on the circle.
- Unit Circle — A circle of radius one unit with its center at the origin. Example: For a point (x, y) on the unit circle, x = cosθ and y = sinθ.
- Sine Function — A function that gives the y-coordinate of a point on the unit circle. Example: sinθ = 0 when θ = 0°, 180°, 360°.
- Cosine Function — A function that gives the x-coordinate of a point on the unit circle. Example: cosθ = 1 when θ = 0°, 360°.
- Tangent Function — A function defined as the ratio of the sine to the cosine. Example: tanθ = 0 when θ = 0°, 180°, 360°.
Exam Tips
Key Definitions to Remember
- A unit circle is a circle with a radius of one unit centered at the origin.
- The sine function represents the y-coordinate of a point on the unit circle.
- The cosine function represents the x-coordinate of a point on the unit circle.
- The tangent function is the ratio of the sine to the cosine.
Common Confusions
- Confusing the maximum and minimum values of sine and cosine.
- Forgetting that the tangent function is undefined at 90° and 270°.
Typical Exam Questions
- What is the maximum value of sinθ? The maximum value of sinθ is 1.
- At what angles is cosθ equal to 0? Cosθ is 0 at 90° and 270°.
- What is the range of values for tanθ? The range of tanθ is –∞ < tanθ < ∞.
What Examiners Usually Test
- Understanding the properties of sine, cosine, and tangent functions.
- Ability to plot and interpret graphs of trigonometric functions.
- Application of trigonometric functions to solve real-world problems.