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Contents
General Solution
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General Solution
The difference between trigonometric equations and algebraic equations is that the former has infinitely many solutions, due to the periodic nature of the functions. (Refer to graphs of trigonometric functions). An algebraic equation, as you would have learned, has a specific number of solutions. So far, we have explained how to solve trigonometric equations for a certain range of angles. For example to solve the equations sin x = 0.5 for a range 0o < x< 360o, we have learnt this:
sin x = 0.5
Basic angle =
30o
x = 30o, 150o
However,
what if we want an angle in the range 1000o
to 1100o? And what if we want to illustrate all the possible
solutions?
This
is where the general solution of trigonometric equations come in. We have
use it to express all possible solutions of any trigonometric equation. In
addition, we can use the general solution to find specific angles.
In
this section, we will introduced the general form for the sine, cosine and
tangent functions, then apply this to some equations.
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