Tri-angled Trig

Why do this problem?

This problem requires students to keep track of an extended algebraic argument, and provides the opportunity to talk about layout of solutions (such as "one equal sign per line, all equal signs aligned").

Students will need to be resilient as the solution method is not entirely clear, and the problem required quite a lot of trigonometric manipulation in order to solve it.

Key questions

• What do we know?
• What is special about $\dfrac{\pi} 2$?
• Which trig relationships might be helpful?
• Can you relate $\sin(\theta + \phi)$ to a trig function involving $\psi$?