January 2014
Intermediate to advanced
144 pages
4h 2m
English
Content preview from Mathematical Formulas for Industrial and Mechanical Engineering
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The graph of y 5
1
sin x
5 cosec x:
–2π –ππ2π0
Properties of the Cosine Function
1. The cosine function is even since cos(2x) 5 cos x, that is, symmetrical about the y-axis
2. The cosine function is continuous
3. The cosine function is periodic with period 2π since cos x 5 cos(x 1 2π)
4. 21 # cos x # 1, that is, the range is [21, 1]
5. The curve cuts the x-axis at 0, 6
π
2
, 6
3π
2
, 6
5π
2
, ...
Graph of cos x:
3π
2
–
3π
2
π
2
0
–
π
2
y
x
Note: The cosi ne graph has the same shape as the sine graph but the former is
shifted by a distance of π=2 to the left on the x-axis.
Graph of y 5 1=cos x 5 sec x:
91Calculus
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