Composite Functions and Trigonometry
Composite functions might look intimidating, but they're just functions within functions. When you see f(g), you substitute the entire g expression into f. So if f = 1/√x and g = 5-x, then f(g) = 1/√.
The key trick is spotting when these composite functions are undefined. Since you can't take the square root of a negative number, 5-x must be greater than 0, which means x must be less than 5.
For right-angled triangles, remember SOHCAHTOA is your best mate. When finding cos p or cos q, you're looking for adjacent/hypotenuse. Use Pythagoras' theorem to find missing sides first - it's usually the stepping stone to solving trigonometric ratios.
Top tip: Always check your triangle measurements make sense using Pythagoras before calculating trig ratios!
The compound angle formula sin = sin p cos q + cos p sin q is essential for A-level success. Once you've found the individual trig ratios, substitute them carefully and simplify step by step.
