### 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.

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

### Resources at Fingertips

This is a vast collection of tutorials, covering the syllabuses of GCSE, iGCSE, A-level and even at undergraduate level. They are organized according to these specific levels.
The major categories are for core mathematics, statistics, mechanics and trigonometry. Under each category, the tutorials are grouped according to the academic level.
This is also an opportunity to pay tribute to the intellectual giants like Newton, Pythagoras and Leibniz, who came up with lots of concepts in maths that we take for granted today - by using them to serve mankind.

Email:

### Stand Out - from the crowd

"There's no such thing as a free lunch."

The best things in nature are free with no strings attached - fresh air, breathtakingly warm sunshine, scene of meadow on the horizon...

Vivax Solutions, while mimicking nature, offers a huge set of tutorials along with interactive tools for free.

Please use them and excel in the sphere of science education.

Everything is free; not even registration is required.

"

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.