Welcome to this short ‘insights video’ showing some of the misunderstandings learners have when solving questions with trigonometric quadratic, or cubic, equations.
Solving ‘trigonometric’ quadratic equations uses the same techniques as ordinary quadratic equations, for example, factorising.
However, there is an added layer of complication because learners also need to apply trigonometric identities or transformations to simplify these equations…
… and when learners apply these identities, they often forget to be as rigorous about the more basic quadratic rules.
They know that the square root of x squared can be either a plus or minus solution. But they often forget to apply the same logic, to say ‘cos squared x’ and only use the positive answer and don’t include the negative solution, so, will have an incomplete answer.
A second misunderstanding around solving trigonometric equations between a range of angles is not to factorise, but cancel terms.
In this expression - students might cancel the cotangent on both sides of the equation…
...But that would lead to valid answers not being given...
...Each term leads to a solution!
And finally, when learners see questions involving two trigonometric terms, to be solved within the specified range. They assume there will always be two valid solutions per term. This is not a rule!
Rather, solutions are cyclical and there can be more than two solutions per term that fit within the range. So learners need to check a good range of answers to see if others fall within the target range.
I hope this short insights video has been useful to you to see some of the challenges learners face when solving these kind of trigonometric equations.
Thank you.
Video transcriptWelcome to this short ‘insights video’ showing some of the misunderstandings learners have when solving questions with trigonometric quadratic, or cubic, equations.
