Solve factored trig equation

A question is this type if and only if the equation is already in factored form (or easily factorisable) such as (1 + tan θ)(5 sin θ − 2) = 0 or cos θ(sin θ − 3 cos θ) = 0, requiring each factor to be set to zero separately.

4 questions · Moderate -0.3

1.05o Trigonometric equations: solve in given intervals
Sort by: Default | Easiest first | Hardest first
Edexcel C2 2009 June Q7
10 marks Moderate -0.3
7. (i) Solve, for \(- 180 ^ { \circ } \leqslant \theta < 180 ^ { \circ }\), $$( 1 + \tan \theta ) ( 5 \sin \theta - 2 ) = 0$$ (ii) Solve, for \(0 \leqslant x < 360 ^ { \circ }\), $$4 \sin x = 3 \tan x .$$
AQA C2 2006 June Q8
11 marks Moderate -0.3
8
  1. Describe the single geometrical transformation by which the curve with equation \(y = \tan \frac { 1 } { 2 } x\) can be obtained from the curve \(y = \tan x\).
  2. Solve the equation \(\tan \frac { 1 } { 2 } x = 3\) in the interval \(\mathbf { 0 } < \boldsymbol { x } < \mathbf { 4 } \boldsymbol { \pi }\), giving your answers in radians to three significant figures.
  3. Solve the equation $$\cos \theta ( \sin \theta - 3 \cos \theta ) = 0$$ in the interval \(0 < \theta < 2 \pi\), giving your answers in radians to three significant figures.
    (5 marks)
AQA C2 2016 June Q8
9 marks Standard +0.3
8
    1. Given that \(4 \sin x + 5 \cos x = 0\), find the value of \(\tan x\).
    2. Hence solve the equation \(( 1 - \tan x ) ( 4 \sin x + 5 \cos x ) = 0\) in the interval \(0 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }\), giving your values of \(x\) to the nearest degree.
  2. By first showing that \(\frac { 16 + 9 \sin ^ { 2 } \theta } { 5 - 3 \cos \theta }\) can be expressed in the form \(p + q \cos \theta\), where \(p\) and \(q\) are integers, find the least possible value of \(\frac { 16 + 9 \sin ^ { 2 } \theta } { 5 - 3 \cos \theta }\). State the exact value of \(\theta\), in radians in the interval \(0 \leqslant \theta < 2 \pi\), at which this least value occurs.
    [0pt] [4 marks]
AQA C3 2007 June Q3
7 marks Moderate -0.8
3
  1. Solve the equation \(\operatorname { cosec } x = 2\), giving all values of \(x\) in the interval \(0 ^ { \circ } < x < 360 ^ { \circ }\).
    (2 marks)
  2. The diagram shows the graph of \(y = \operatorname { cosec } x\) for \(0 ^ { \circ } < x < 360 ^ { \circ }\). \includegraphics[max width=\textwidth, alt={}, center]{9fd9fa54-b0e6-413d-8645-de34b99b859a-03_609_1045_559_479}
    1. The point \(A\) on the curve is where \(x = 90 ^ { \circ }\). State the \(y\)-coordinate of \(A\).
    2. Sketch the graph of \(y = | \operatorname { cosec } x |\) for \(0 ^ { \circ } < x < 360 ^ { \circ }\).
  3. Solve the equation \(| \operatorname { cosec } x | = 2\), giving all values of \(x\) in the interval \(0 ^ { \circ } < x < 360 ^ { \circ }\).
    (2 marks)