Solving Trigonometric Equations

E.g.1


sinegraph

 

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

sinegraph

 

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.

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