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two students were discussing a problem in which a distant object was seen through an angle of 2.3 degrees. One student found the distance to the object using the tangent of the angle, and the other had the same answer using the sine of the angle. Write a paragrapgh explain how this was possible

Guest May 17, 2017
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well you need at least one distance measurment i would think to even start this, but i assume it is irrelevent as they want you to compare sine and tangent. so sine is opposite over hypotenuse and tangent is opposite over adjacent. both have opposite in the fomula so use that as your basis for comparing them

Guest May 17, 2017
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When angles are very small the following approximations hold:

 

sin(theta) ≈ theta

tan(theta) ≈ theta

(Where theta is measured in radians), so sin and tan return very nearly the same value.

 

2.3 degrees is 2.3*pi/180 radians → 0.0401 radians. This is small!

 

More precisely:

 

sin(2.3degrees) ≈ 0.040131792533

 

tan(2.3degrees) ≈ 0.040164148968

Alan  May 17, 2017

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