Trigonometry — common mistakes

Always check the required range for your solutions (e.g., $0 \le x \le 2\pi$ or $-180^\circ \le x \le 180^\circ$) and whether the answer should be in radians or degrees. Forgetting to find all solutions within the range is a very common way to lose marks. Also, when proving an identity, you must start from one side and manipulate it algebraically until it looks identical to the other side. Do not 'solve' it like an equation.

The question will specify. If it gives a range in degrees, use degrees. If the range is in terms of π, use radians. If no range is given (e.g., in a pure identity proof), it doesn't matter, but radians are standard practice at this level. If the question involves calculus, you MUST use radians.

Look at the other terms in the equation. If the equation also contains a 'cos A' term, use the 2cos²A - 1 form to create a quadratic in cos A. If it contains a 'sin A' term, use the 1 - 2sin²A form. If it contains both, you might need a different approach!

You cannot easily solve an equation like $3sin(x) + 4cos(x) = 2$ without the harmonic form. It allows you to reduce two trigonometric terms into one, which is solvable. It's also the only straightforward way to find the maximum or minimum value of such a combination.

There are two common errors. First, your calculator only gives the 'principal value'. You must use this first answer to find all other possible solutions within the given range (e.g., using CAST diagrams or graph sketches). Second, if you squared both sides of an equation at any point, you may have introduced extra solutions that don't work in the original equation, so you must check them.