9709 · 3.3
Trigonometry
P3 trigonometry gives you a powerful toolkit of identities to simplify and solve equations that mix different trig functions. By converting expressions into simpler forms, we can find solutions or determine maximum and minimum values.
Need to know
What you need to know
- Pay close attention to the signs in the compound angle formulae. For $\cos(A+B)$, the sign on the right-hand side is negative.
- The three different forms for $\cos(2A)$ are crucial. Choose the form that best simplifies your equation. For example, if your equation also contains $\cos A$, use the $2\cos^2 A - 1$ form to create a quadratic in $\cos A$.
Explanation
Unlocking Trig Equations
- Master the core identities, including the Pythagorean set (sin²θ + cos²θ ≡ 1, etc.) and the compound angle formulae. These are your fundamental tools for rewriting expressions.
- Learn to combine a sin(x) + b cos(x) into a single sine or cosine wave, R sin(x + α). This simplifies finding the amplitude (R) and phase shift (α) of the combined wave.
- When solving for an angle, like x = arcsin(k), remember that your calculator gives only one answer (the principal value). You must use the unit circle or graphs to find all other solutions in the required range.
- Always work in radians unless a question specifies degrees. Radians are the natural unit for angles in calculus, which is deeply connected with trigonometry at this level.