E: Trigonometry: Use trigonometric functions to solve problems in context, including problems involving vectors, kinematics and forces.

The idea

This topic involves applying trigonometric functions to model and solve real-world problems. You might resolve a force into components using sine and cosine, analyse projectile motion by separating horizontal and vertical components, or find the resultant of vectors given as magnitudes and directions. For example, a force of 10 N at 30° to the horizontal has a horizontal component 10cos30° and a vertical component 10sin30°. You need to interpret the context, set up equations, and solve using trigonometry. Problems may require the sine or cosine rule in triangles, or using trigonometric identities to simplify. Assessment focuses on correct modelling, accurate calculations, and clear communication of the solution in context.

What earns the marks

• Correctly resolve vectors or forces into perpendicular components using sine and cosine.
• Apply the sine and cosine rules to solve problems involving non-right-angled triangles in context.
• Interpret kinematic problems by separating motion into horizontal and vertical components and applying trigonometry.
• Combine vector components to find resultant magnitudes and directions using Pythagoras and inverse trigonometric functions.
• Communicate the solution clearly, including units and interpretation in the context of the problem.

Common mistakes and how to put them right

• Confusing which component uses sine and which uses cosine when resolving a vector.

  Put it right: Draw a diagram and identify the angle with the horizontal; the adjacent component uses cosine, the opposite uses sine.

• Misapplying the sine or cosine rule by using the wrong side or angle.

  Put it right: Label the triangle clearly and match the rule to the given information (e.g., cosine rule for SAS or SSS).

• Using incorrect signs for vector components depending on their direction.

  Put it right: Define a positive direction for horizontal and vertical axes and ensure components acting in the opposite direction are negative.

Exam tips

• Draw a clear diagram for any problem involving vectors, forces, or motion; label all known angles and magnitudes.
• Check that your final answer is reasonable in the context (e.g., a force magnitude cannot be negative).
• Show all steps of your working, including the trigonometric equations you set up, to gain method marks even if the final answer is incorrect.