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### Number and algebra

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# Tri-angled Trig

### Why do this problem?

### Key questions

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### Curvy Equation

### Digital Equation

### Euler's Totient Function

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Age 16 to 18

Challenge Level

- Problem
- Student Solutions
- Teachers' Resources

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.

- 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 $\psi$?

This problem asks you to use your curve sketching knowledge to find all the solutions to an equation.

Can you find a three digit number which is equal to the sum of the hundreds digit, the square of the tens digit and the cube of the units digit?

How many numbers are there less than $n$ which have no common factors with $n$?