# Mathematics

### Solving Trigonometric Equations

E.g.1

Solve sin x = 0.5 for 0 ≤ x ≤ 360
sin x = 0.5
x = 300
Since y = 0.5 line crosses the sine curve at two points, there are two solutions.
Now, look at the symmetry of the graph; the two values of x are 300 and 1500.
x = 30 and 150.

E.g.2

Solve cos x = -0.5 for 0 ≤ x ≤ 360
cos x = -0.5
x = 1200
Since y = -0.5 line crosses the sine curve at two points, there are two solutions.
Now, look at the symmetry of the graph; the two values of x are 1200 and 2400.
x = 120 and 240.

E.g.3

Solve sin (x +10) = 0.5 for 0 ≤ x ≤ 360
From example 1,
(x + 10) = 300
There are two values for (x +10) that satisfy the equation; they are 300 and 1500
x + 10 = 30 or x + 10 = 150
x = 20 or x = 140

E.g.4

Solve 1 + 2 sin x = 2 for 0 ≤ x ≤ 360
2 sin x = 1
sin x = 0.5
From example 1,
x = 300
There are two values for x that satisfy the equation; they are 300 and 1500
x = 30 or x = 150.

#### Solving Equations - interactive

You can animate the y=a line by clicking the play button or move the slider to a point you want it to be at.

Now, in order to complement what you have just learnt, work out the following questions:

1. Solve 2 sin x = 1.5 for 0 ≤ x ≤ 360
2. Solve 1 + 3 cos x = 2 for 0 ≤ x ≤ 360
3. Solve sin (2x - 10) = 0.7 for 0 ≤ x ≤ 360
4. Solve tan (x -30) = 0.7 for 0 ≤ x ≤ 360
5. Solve cos (2x -20) = 0.5 for 0 ≤ x ≤ 360
6. Solve sin2 x = 0.25 for 0 ≤ x ≤ 360
7. Solve sin 2x = 0.5 for 0 ≤ x ≤ 360
8. Solve 1 + 3 sin 2x = 2 for 0 ≤ x ≤ 360

Maths is challenging; so is finding the right book. K A Stroud, in this book, cleverly managed to make all the major topics crystal clear with plenty of examples; popularity of the book speak for itself - 7th edition in print.

### Recommended - GCSE & iGCSE

This is the best book available for the new GCSE(9-1) specification and iGCSE: there are plenty of worked examples; a really good collection of problems for practising; every single topic is adequately covered; the topics are organized in a logical order.

### Recommended for A Level

This is the best book that can be recommended for the new A Level - Edexcel board: it covers every single topic in detail;lots of worked examples; ample problems for practising; beautifully and clearly presented.