1. Investigate the built-in trigonometry functions in Excel. Verify the identity sin2(8) + cos2(8) -
Make five columns and the headings: angle in degrees, angle in radians, sin(e), cos(8), and,
sin2(8) + cos2(8) - 1. Let angles range from Oto 360.
Add a column to show that sin(20)=2sin(@)cos(8)
2. The small-angle approximation is a useful simplification of the basic trigonometric functions which
approximately true in the limit where the angle approaches zero. Two expressions that result from the
small-angle approximation are:
sin(8)=0 and cos(8) R 1
where e is the angle in radians.
The small angle approximation is useful in many areas of physics, including mechanics,
electromagnetics, optics (where it forms the basis of the paraxial approximation), cartography,
astronomy, and so on.
Investigate the error in the small angle approximation. Specifically:
1) Plot e and sin(e) on the same axes for values of e ranging from -1 to 1 radians.
2) Plot 1 and cos(8) on the same axis for values of e ranging from -1 to 1 radians.
3) Determine the value of 0 to the nearest 0.01 radian so that the % error between the approximation
and the exact trigonometric function is less than 1% and less than 5%. What is corresponding angle in
Define the percent error as:
(approximate - exact)
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