Trigonometry (A2 Unit 4: Applied Mathematics B) — WJEC A-Level Mathematics
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Trigonometry (A2 Unit 4: Applied Mathematics B) explained
Trigonometric functions sin θ, cos θ, and tan θ are indispensable across mechanics for resolving vectors, analysing inclined planes, and modelling periodic motion.
Read the full explanation
When resolving a force F inclined at angle θ to an axis, the adjacent component is F cos θ and the opposite component is F sin θ. On an inclined plane at angle α to horizontal, weight W = mg resolves into mg sin α down the slope and mg cos α perpendicular into the slope. In kinematics, projectile velocities resolve into horizontal u cos θ and vertical u sin θ. Trigonometric identities such as sin²θ + cos²θ = 1 and sec²θ = 1 + tan²θ help eliminate angles in trajectory equations.
Your focus
- Resolve force and velocity vectors into orthogonal components using trigonometric functions.
- Analyse forces on inclined planes using parallel (mg sin α) and perpendicular (mg cos α) components.
- Apply trigonometric identities to eliminate time and angle parameters in kinematic models.
Trigonometry (A2 Unit 4: Applied Mathematics B) exam tips
Marking Points
- correctly resolving forces or velocities into orthogonal trigonometric components
- resolving weight on an inclined plane into mg sin α parallel and mg cos α perpendicular
- applying trigonometric equations or identities to solve multi-step mechanics problems
Examiner Tips
- 💡Check calculator angle mode (degrees vs radians) before evaluating trigonometric terms.
- 💡Remember: weight parallel to an incline of angle α is ALWAYS mg sin α, and perpendicular is mg cos α.
Common Mistakes
- swapping sine and cosine when resolving weight on an inclined plane (using cos for parallel instead of sin)
- evaluating trigonometric functions in radian mode when angles are given in degrees, or vice versa