The Goal

Solve the following equation for t:

The Mistake

Find the mistake:

(Roll the mouse over the math to see a hint in red)

The Correction

(Roll the mouse over the area above to see the correction in blue)

An Explanation

It is not true that sin(AB) is equal to sin(A)sin(B) - there is no nice formula for sin(AB). The correct method is to set the argument of the sine, namely (π/6)t, equal to the angles for which sine takes the value 0, namely all integer multiples of π. It is then easy to solve the resulting equation and identify the solutions for which 0 ≤ t ≤ 24.
(There is a formula for sin(A)sin(B):

This formula is one of the prosthaphaeretic formulas.)