Trigonometry in Paper 1 means solving equations in a given range, proving identities, working with graphs and transformations, and using exact values. The reports show that students usually know the methods. They lose marks for missing solutions, presentation, and accuracy. This guide collects what Cambridge examiners say students get wrong, based on recent reports.
Summarised in our own words from a reading of the examiner reports.
Mistakes that cost marks
- Missing solutions. This is the most repeated comment. Students find the principal value and stop, forget the negative angles in a range that includes them, lose solutions by cancelling a common factor, or give only two answers when four were possible. Reports say that students often did not recognise that the interval was from −180° to 180°.
- One root of a square. When an equation reduces to cos²θ = k, both the positive and the negative square root are needed. Students also forget to take the square root at all, or to cube root after finding the cube of a function.
- The wrong units or accuracy. Answers in degrees when the range was in radians (or the opposite), answers in radians given to one decimal place when 3 significant figures were asked for, and rounding errors from rounding 2x before dividing by 2.
- Identities. Students attempted to square each term, failed to use cos²θ = 1 − sin²θ correctly, did not multiply through by the common denominator, or lost a factor of 2 when reaching the printed answer in a "show that" question. Using the identity to form an equation in a different function than the question needed sometimes led to a lot of extra algebra.
- Not quoting the relationship. Reports say that in proof questions students should quote the relationships they are using at each stage. In some questions, the step of forming a common denominator needs to be shown.
- Quadratics in disguise. The equation did not become a three-term quadratic, or the method for solving the quadratic was not shown. Candidates who found the solution without factorising lost the second method mark.
- Wrong transformation language. The transformation questions were often described in an incomplete or incorrect way, for example with a stretch factor of ½ instead of 2, or a translation in the wrong direction.
- Sketching. Part of the trigonometry questions asks for graphs, and many students struggled to draw the requested graph or to interpret it.
- Combining angles. Losing the minus sign when combining angles and working out a non-exact answer when the question wanted an exact one.
What examiners advise
- List all the solutions in the range and check how many you expect before you stop. Reports advise checking that you have obtained all possible solutions.
- Show the method for any equation that reduces to a quadratic, including factorising.
- State the relationship you use in a proof or identity, and show the stage where the denominator is combined.
- In "show that" questions show every line that leads to the printed result, without omitting the factor that would make it work.
- Work in the unit the question uses, and give answers in the required accuracy.
Habits that help
- Sketch the graph of the function in the given range to see how many solutions there are.
- Think about the quadrant. The sign of sine, cosine and tangent tells you which angles are possible.
- Know the exact values of common angles in both degrees and radians.
Questions students ask
Why do I lose marks on trigonometric equations even when my method is right?
Missing solutions. Examiners call this the most repeated comment. Students find the principal value and stop, forget negative angles in a range such as −180° to 180°, lose solutions by cancelling a common factor, or give two answers when four were possible. Work out how many solutions to expect before you stop.
Do I need both the positive and negative square root in cos²θ = k?
Yes. When an equation reduces to cos²θ = k, both roots are needed. Students also forget to take the square root at all.
How do I get full marks on a "show that" trigonometric identity question?
Quote the relationship you use at each stage, such as cos²θ = 1 − sin²θ, show the step where the common denominator is formed, and show every line up to the printed result without dropping a factor of 2.
Should my trig answers be in degrees or radians?
Use the unit of the range in the question and give the accuracy asked for. Reports record answers in degrees when the range was in radians, and rounding errors from rounding 2x before dividing by 2.
What if a trigonometric equation turns into a quadratic?
Show the method for solving the quadratic, including the factorisation. Candidates who found the solutions without showing the factorising lost the second method mark.
Practice this topic
Ready to try some? Work through past paper questions on this topic one at a time. Attempt each question fully first, and open the mark scheme only afterwards.