Loading....
Coupon Accepted Successfully!

 

Trigonometric Equations

Definition:- Equations involving trigonometric functions as variables are called trigonometric equations.


Recollect the property of sin x and cos x repeating (periodic) after 2π and tan x repeating after an interval of π.
Hence trigonometric equations will have infinite solutions.

Eg: cos x = 0


Among these innumerable answers, the solutions for which 0 x 2 π are called principal solution.

Example:
Find the principal solutions of the equation
Principal solutions are
The expression involving integer
'n' which gives all the solution for the trigonometric equation is called general solution

Example:


General Solution (1):

 

Example:
Solve: 

Solution:
Principal solutions are
Sin is negative in III & IV quadrants


Note:- You can use any one of the principal solutions

General Solution(2):


Solution:-

 

Example:
Solve:

Solution:

Principal solution x = 0  (cos 0 = 1)
General solution is
x = 2nπ ± 0


General Solution(3):
Let tan x = tan y, where y is the principal solution


Example:
Solve:

Solution:
Principal Solutions
[Recollect tan is positive in I & III quadrants]
General solution is

Note:- For solving trigonometric equations involving sec, cosec and cot functions, convert them to sin, cos or tan and then use the relevant formula.

Example 1:
Solve:

Solution:

When
General Solution:
When assume β to be the principal value, ie (can be obtained from trigonometric Tables. general solution:


Example 2:


Solution:

[Note Principal solution for ]


Example 3:
Solve:

Solution:





Test Your Skills Now!
Take a Quiz now
Reviewer Name