Comprehensive assessment covering reciprocal trig functions, identities, compound and double angles, t-formulas, solving equations, and inverse trig functions.
1. Find the exact value of $\cos(\\frac{7\\pi}{6})$. (1 mark)
2. If $\sin\\theta = -\\frac{4}{5}$ and $\\pi < \\theta < \\frac{3\\pi}{2}$, find $\cot\\theta$. (2 marks)
3. Prove that $\\tan\\theta + \\cot\\theta = \\sec\\theta \\csc\\theta$. (2 marks)
4. Find the exact value of $\cos(15°)$. (2 marks)
5. If $\tan\\theta = 3$, find $\tan(2\\theta)$. (2 marks)
6. Express $\\sin\\theta + \\sqrt{3}\\cos\\theta$ in the form $R\\sin(\\theta + \\alpha)$. (3 marks)
7. Solve $2\\cos^2\\theta + \\cos\\theta - 1 = 0$ for $0 \\le \\theta < 2\\pi$. (3 marks)
8. Solve $\tan(3\\theta) = 1$ for $0 \\le \\theta < \\pi$. (3 marks)
9. Evaluate $\sin^{-1}(\\sin\\frac{2\\pi}{3})$. (2 marks)
10. Sketch $y = \\cos^{-1}x$, labelling domain, range, and key points. (3 marks)