Solve trigonometric equation with approximate values

A question is this type if and only if it requires solving a trigonometric equation to find approximate/decimal solutions (to a specified number of decimal places) in a given interval.

2 questions · Moderate -0.6

1.05o Trigonometric equations: solve in given intervals
Sort by: Default | Easiest first | Hardest first
CAIE P1 2015 June Q8
9 marks Moderate -0.3
The function \(\text{f} : x \mapsto 5 + 3\cos(\frac{1}{3}x)\) is defined for \(0 \leqslant x \leqslant 2\pi\).
  1. Solve the equation \(\text{f}(x) = 7\), giving your answer correct to 2 decimal places. [3]
  2. Sketch the graph of \(y = \text{f}(x)\). [2]
  3. Explain why \(\text{f}\) has an inverse. [1]
  4. Obtain an expression for \(\text{f}^{-1}(x)\). [3]
Edexcel C2 Q9
10 marks Moderate -0.8
  1. Sketch, for \(0 \leq x \leq 2\pi\), the graph of \(y = \sin\left(x + \frac{\pi}{6}\right)\). [2]
  2. Write down the exact coordinates of the points where the graph meets the coordinate axes. [3]
  3. Solve, for \(0 \leq x \leq 2\pi\), the equation \(\sin\left(x + \frac{\pi}{6}\right) = 0.65\), giving your answers in radians to 2 decimal places. [5]