If an equation involves sin2θ or cos2θ then it is a quadratic trigonometric equation
These can be solved by factorising and/or using trigonometric identities (see Trigonometry – Simple Identities)
As a quadratic can result in two solutions, will need to consider whether each solution exists and then find all solutions within a given interval for each
You may be asked to use degrees or radians to solve trigonometric equations
Make sure your calculator is in the correct mode
Remember common angles
90° is ½π radians
180° is π radians
270° is 3π/2 radians
360° is 2π radians
Sketch the appropriate sin, cos, tan graph to ensure you find ALL solutions within the given interval, and be super-careful if you get a negative solution but have a positive interval.
For example, for an equation, in the interval 0° ≤ x ≤ 360°, with solution sin x = ‑¼ then sin‑1(‑¼) = -14.5 (to 1d.p.), which is not between 0 and 360 – by sketching the graph you’ll be able to spot the two solutions will be 180 + 14.5 and 360 ‑ 14.5.
Lucy has been a passionate Maths teacher for over 12 years, helping to engage interest and develop confidence in the subject at all levels. As Head of Department and Director of Maths, Lucy has advised schools across both academy trusts and an entire city, where her role was to support and coach teachers to improve Maths teaching for all.