Know the three curve shapes
and wave between and with period ( is shifted left by ); repeats every and has vertical asymptotes at
Use symmetry to get the second solution
In – most equations have two solutions. For the second is (first); for it is (first).
Key values to remember
: max at , min at , zero at . : max at , min at .
Drawn from real examiner reports.
Calculator in the wrong angle mode
There was evidence of students working in gradians (or radians) rather than degrees, giving nonsense trig values.
Noted in the November 2024 Paper 2H report introduction.
Giving only one solution in the range
The calculator returns just one angle; the symmetry of the curve gives a second solution in – that students often omit.
(general exam technique)
Not using the trig functions correctly
Mislabelling or misusing , and — the summary reminds students to know how to use the trigonometric functions correctly.
From the June 2024 Paper 2H summary.
Using 180° − x for a cosine equation
The symmetry rules differ: for the second solution is (first), but for it is (first). Using for cosine gives the wrong angle.
Quoting a negative calculator angle
For the calculator shows , outside –. Use the curve instead: and .
Sketch the curve and draw the line y = k
Sketch (or ), draw the horizontal line , and read off every crossing inside the range — this guarantees you find all the solutions.
Set the calculator to degrees
Before any trig work, check the mode indicator shows DEG (not RAD or GRAD). A wrong mode turns every value into nonsense and is easy to miss under exam pressure.
Expect two solutions in the range
In –, and equations usually have two solutions. If you have written only one, use the symmetry of the curve to find its partner before moving on.
Common calculator error in trig questions?
Using the graph of , solve for .
