Test your understanding of double and half angles, t-formulas, and the auxiliary angle method.
1. If $\cos\\theta = \\frac{12}{13}$ and $0 < \\theta < \\frac{\\pi}{2}$, find $\sin(2\\theta)$. (2 marks)
2. Find the exact value of $\sin(22.5°)$. (2 marks)
3. If $t = \\tan\\frac{\\theta}{2} = \\frac{1}{3}$, find $\cos\\theta$. (2 marks)
4. Express $3\\sin\\theta + 4\\cos\\theta$ in the form $R\\sin(\\theta + \\alpha)$. (3 marks)