Find general solution of trig equation

A question is this type if and only if it asks for the general solution (all solutions) of a trigonometric equation, typically expressed in terms of n or involving 2πn.

5 questions · Standard +0.3

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AQA FP1 2013 January Q3
8 marks Standard +0.3
3
  1. Find the general solution of the equation $$\sin \left( 2 x + \frac { \pi } { 4 } \right) = \frac { \sqrt { 3 } } { 2 }$$ giving your answer in terms of \(\pi\).
  2. Use your general solution to find the exact value of the greatest solution of this equation which is less than \(6 \pi\).
AQA FP1 2010 June Q3
5 marks Moderate -0.3
3 Find the general solution, in degrees, of the equation $$\cos \left( 5 x - 20 ^ { \circ } \right) = \cos 40 ^ { \circ }$$
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AQA FP1 2014 June Q8
9 marks Standard +0.8
8
  1. Find the general solution of the equation $$\cos \left( \frac { 5 } { 4 } x - \frac { \pi } { 3 } \right) = \frac { \sqrt { 2 } } { 2 }$$ giving your answer for \(x\) in terms of \(\pi\).
  2. Use your general solution to find the sum of all the solutions of the equation \(\cos \left( \frac { 5 } { 4 } x - \frac { \pi } { 3 } \right) = \frac { \sqrt { 2 } } { 2 }\) that lie in the interval \(0 \leqslant x \leqslant 20 \pi\). Give your answer in the form \(k \pi\), stating the exact value of \(k\).
    [0pt] [4 marks]
AQA FP1 2016 June Q4
2 marks Standard +0.3
4
  1. Given that \(\sin \frac { \pi } { 3 } = \cos \frac { \pi } { k }\), state the value of the integer \(k\).
  2. Hence, or otherwise, find the general solution of the equation $$\cos \left( 2 x - \frac { 5 \pi } { 6 } \right) = \sin \frac { \pi } { 3 }$$ giving your answer, in its simplest form, in terms of \(\pi\).
  3. Hence, given that \(\cos \left( 2 x - \frac { 5 \pi } { 6 } \right) = \sin \frac { \pi } { 3 }\), show that there is only one finite value for \(\tan x\) and state its exact value.
    [0pt] [2 marks]
AQA FP1 2005 January Q6
8 marks Standard +0.3
6 The angle \(x\) radians satisfies the equation $$\cos \left( 2 x + \frac { \pi } { 6 } \right) = \frac { 1 } { \sqrt { 2 } }$$
  1. Find the general solution of this equation, giving the roots as exact values in terms of \(\pi\).
  2. Find the number of roots of the equation which lie between 0 and \(2 \pi\).