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Arrange the following assortment of angle measures in ascending order; 210°, 350°, 2π, 5.3 radians, 90°, 1.7 radians, π/3 , 1 radian, 55°, π.

I only just started learning about angle measurements and so I'm struggling with this question. How would I correctly place them in ascending order? Any help is appreciated.

Savannah
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  • What do you know about the constant of proportionality between degrees and radians? – Andrew Chin Jan 06 '20 at 18:45
  • I was taught that 2π radians = 360°, π radians = 180°, and 1 radian = 57.295.. = 60°. – Savannah Jan 06 '20 at 18:47
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    If you know that there are $2\pi$ radians for $360^{\circ}$, then how many radians in $1^\circ$? How do you compare measures that are in different units? – Andrew Chin Jan 06 '20 at 18:49
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    To point you in a similar direction, which is longer, $2$ inches, or $5$ centimetres? $0.97$ miles, or $1450$ metres? – Andrew Chin Jan 06 '20 at 19:00

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Four angles are in degrees: 210,350,90,55. Three are in radians: 5.3,1.7,1. Another three are also in radians but expressed in terms of $\pi$.

So you need to convert them all to some common unit, say radians. Thus multiply each of the degree values by $\pi/180$ and use $\pi=3.1416$ to convert the multiples of $\pi$. Then you should be able to see the correct order.

almagest
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