Key values to remember
: max at , min at , zero at . : max at , min at .
Use symmetry to get the second solution
In – most equations have two solutions. For the second is (first); for it is (first).
Know the three curve shapes
and wave between and with period ( is shifted left by ); repeats every and has vertical asymptotes at
Drawn from real examiner reports.
Giving only one solution in the range
The calculator returns one angle; students often forgot the curve's symmetry gives a second solution in –.
A standard examiner caution on trig-graph questions.
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 a recent higher-tier exam introduction.
Not using the trig functions correctly
Mislabelling or misusing , , — examiners ask students to "know how to use the trigonometric functions correctly".
From a recent higher-tier exam.
Quoting the negative calculator angle
For the calculator gives , outside –. Add to bring it into range: and . Never leave a negative angle as a final answer in the stated range.
Adding 360° for tan instead of 180°
repeats every , so its two solutions in – are exactly apart. Adding the sine/cosine period of instead misses the second tan solution.
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.
Keep full accuracy until the end
Carry the unrounded inverse-trig value through the symmetry step and round only at the end. Rounding to first pushes the partner off by nearly a degree and loses the accuracy mark.
Extend the range with the period
For a wider range such as –, take each solution in – and add the period: for /, for . So and also give and .
Common calculator error in trig questions?
State the maximum value of and the value of in where it occurs, and write down the period of .
