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Contents
Sine Function
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Sine Function
Say we are given the equation sin 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 = 180on + (-1)n sin-1k Note: sin-1k must be in the principal range, between -p/2 and p/2.
Decide whether to use degrees or radians and stick to it throughout your
solution
Example: Find
the general solution of
(i) sin x = 0.5
(ii) sin 2x = 0.75
Solution:(i)
sin x = 0.5
x = np
+ (-1)n sin-10.5
= np
+ (-1)n (p/6)
(ii)
sin 2x = 0.75
2x = np
+ (-1)n 0.848
x = np/2
+ (-1)n 0.424
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q
= np
+ (-1)n sin-1k
