TRIGONOMETRY – general solutions

 

The general solutions are used to solve trigonometric equations.

 

·          Rearrange the equation till you are left with just the trig function (eg , or , or  equalling a number.

·          Use your calculator to find what angle this represents. This angle is known as the Principle Value (PV).

·          Substitute into the general solution, remembering that the  stands for the whole angle part of the trig function (eg if the question was , then  ).

·          Rearrange until you have made  the subject

·          Substitute suitable values for n until your solutions go beyond the range given in the question.

·          Work throughout in the units (degrees/radians) given by the question because the numbers given will usually work out nicely then.

 

General Solutions in degrees

 

                             ,  

                             , 

                             , 

 

eg: Find the solutions to .

 

Rearrange first, then find PV:

 

           

 

Substitute into General Solution for Cos and rearrange:

 

           

 

use n values to find solutions in the given range:

 

           

 

General Solutions in radians (NB remember to work in fractions of π as much as possible)

 

                             ,  

                             , 

                             , 

 

eg Find the solutions to .

 

           

 

           

 

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