Trigonometry (Continued)


   
 
Theorem 4
General solution of acosq + bsinq = c
 
Method I
 
-----(i)
 
Put a = r cos a, b = r sin a -----(ii)
 
 
 
(i) can be written as
 
 
 
 
 
From (ii) and (iii), we obtain the auxiliary angle a.
 
Now c and r are known, and from (iv) the general solution of q is determined.
 
Method II
 
a cos q + b sin q = c -----(i)
 
 
(i) can be written as
 
 
or a (1- t2) + 2bt - c (1+t2) = 0
 
This is a quadratic in 't' and can be solved.
 
 
Examples:
 
Find the general solution of the following equations:
 
 
 
 
4) cos q - cos q = 1
 
Suggested answer:
 
 
 
We get,
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
4) cos q - sin q = 1
 
 
 
 
 
 
 
 
 
 
 
 
 
Note:
 
 
So the general solution is the same as for sin q.
 
 
 
So the general solution is the same as for cos q.
 
 
 
 
So the general solution is the same as for tan q.
 
i.e., if cot q = k, then q = np + a.
 
  
     
   
Get unlimited tutoring in Math, English, Physics, Chemistry, Biology, Algebra, Geometry and all other subjects at $99.99 per month!

(100% money-back guarantee)

Customer Care

Click to get customer service, technical support and subscription help.

Customer Care Chat


Refer-A-Friend

Get One Month Free!
When you refer a friend