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Contents
Cosine Function
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Cosine Function
Say we are given the equation cos x = k, where k is constant and between 1 and -1 inclusive. Graphically, this equation is illustrated as such (in radians):
The black dots indicate the co-ordinates of a solution. As you can see, there are infinitely many solutions, 8 of which are illustrated in the graph. The general solution is given by:
or, in degrees, q = 360on + cos-1k and 360on - cos-1k Note: cos-1k must be in the principal range, between 0 and p.
Decide whether to use degrees or radians and stick to it throughout your
solution
Example: Find
the general solution of cos (x + 40o) = 0.5
Solution:
cos (x + 40o) = 0.5
x + 40o = 360on + 60o or
x + 40o = 360on - 60o
x = 360on +20o
x = 360on - 100o
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q
=
2np
+ cos-1k
and
2np
- cos-1k
