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.

3 questions · Standard +0.1

1.05o Trigonometric equations: solve in given intervals
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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 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 \(2 \pi\).