A particle is following a circular path and is observed to have an angular displacement of 10.3°.

 Question 3

A particle is following a circular path and is observed to have an angular displacement of 10.3°.

(a) Express this angle in radians (rad). Show your working and give your answer to three significant figures. [2]

 

 

(b) (i) Determine tan10.3° to three significant figures.

 

(ii) Hence calculate the percentage error that is made when the angle 10.3°, as measured in radians, is assumed to be equal to tan10.3°.

[3]

 

 

Reference: Past Exam Paper – November 2004 Paper 4 Q1

 

 

Solution:

(a)

 θ (rad) = 2π × (10.3/360)                    

θ (rad) = 0.180 rad                             

 

 

(b) (i) tan θ = 0.182                            

 

(ii)

{Difference between θ and tanθ = 0.182 – 0.180 = 0.002}

 

percentage error = (0.002/0.180) x 100                                

percentage error = 1.1 (%)