Study Notes
Trigonometric equations involve using trigonometric functions to find unknown angles or sides in triangles, especially non-right-angled ones.
- Cosine Rule — used to calculate unknown sides or angles in non-right-angled triangles. Example: For triangle ABC, c² = a² + b² - 2ab * cos(C).
- Sine Rule — relates the sides of a triangle to the sines of its angles. Example: a/sin(A) = b/sin(B) = c/sin(C).
- Unit Circle — a circle with a radius of one, used to define trigonometric functions. Example: The angle 130° is in the 2nd quadrant.
- CAST Diagram — helps determine the sign of trigonometric functions in each quadrant. Example: In the first quadrant, all trigonometric functions are positive.
Exam Tips
Key Definitions to Remember
- Cosine Rule: c² = a² + b² - 2ab * cos(C)
- Sine Rule: a/sin(A) = b/sin(B) = c/sin(C)
- Unit Circle: Circle with radius 1 used for trigonometric functions
- CAST Diagram: Tool to determine the sign of trig functions in quadrants
Common Confusions
- Mixing up the sine and cosine rules
- Incorrectly identifying the quadrant for an angle
Typical Exam Questions
- Solve the equation for angles between 0° and 180°? Use the appropriate trigonometric rule and check the quadrant.
- Determine the quadrant for an angle of 250°? Third quadrant, as 180° < 250° < 270°.
- Use the CAST diagram to find the sign of sin(150°)? Positive, as it is in the second quadrant.
What Examiners Usually Test
- Ability to apply the sine and cosine rules correctly
- Understanding of the unit circle and CAST diagram
- Solving trigonometric equations within specified angle ranges