Solving basic trigonometric equations beyond the range 0 to 360 degrees

A complete lesson on solving equations of the form sinx = a, asinx = b and asinx + b = 0 (or using cos or tan) for any range.
Designed to come after pupils have spent time solving equations in the range 0 to 360 degrees, and are also familiar with the cyclic nature of the trigonometric functions. See my other resources for lessons on these topics.

I made this to use with my further maths gcse group, but could also be used with an A-level class.

Activities included:

Stater:
A set of 4 questions to test if pupils can solve trigonometric equations in the range 0 to 360 degrees.

Main:

• A visual prompt to consider solutions beyond 360 degrees. followed by a second example (see cover image) that will lead to a “dead-end” for pupils.
• Slides to define principal values for sine, cosine and tangent, followed by a summary of how to solve equations for any range.
• Three example problem pairs to model methods and then get pupils trying. Includes graphical representations to help pupils understand.
• A worksheet with a progression in difficulty and a challenging extension to create equations with a required number of solutions.

Plenary:
A prompt to discuss solutions to the extension task.