 # Trigonometric Functions in Excel and Small Angle Approximation

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## Transcribed Text

1. Investigate the built-in trigonometry functions in Excel. Verify the identity sin2(8) + cos2(8) - 1 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 is 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. 02 2) Plot 1 and cos(8) on the same axis for values of e ranging from -1 to 1 radians. 2 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 degrees? Define the percent error as: (approximate - exact) %error - x 100% exact

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