# TrigonometryFind angles when circumference is divided into 5 unequal parts

#### Ragnarok

##### Member
Hello, I am using a very old textbook from 1895, Loney's Trigonometry, which poses the following problem:

If the circumference of a circle be divided into 5 parts, which are in A.P., and if the greatest part be 6 times the least, find in radians the magnitudes of the angles that the parts subtend at the centre of the circle.

The answers are given as $$\displaystyle \frac{4\pi}{35},\frac{9\pi}{35},\frac{14\pi}{35}, \frac{19\pi}{35},\frac{24\pi}{35}$$ radians.

The trouble is that I have no idea what is meant by "5 parts, which are in A.P.". There is no diagram and the only reference to points A and P I can find is in a much earlier diagram, where AP is an arc subtending an angle of one radian. Does anyone have any ideas, based on the specifications of the problem? Thank you!

#### Prove It

##### Well-known member
MHB Math Helper
Hello, I am using a very old textbook from 1895, Loney's Trigonometry, which poses the following problem:

If the circumference of a circle be divided into 5 parts, which are in A.P., and if the greatest part be 6 times the least, find in radians the magnitudes of the angles that the parts subtend at the centre of the circle.

The answers are given as $$\displaystyle \frac{4\pi}{35},\frac{9\pi}{35},\frac{14\pi}{35}, \frac{19\pi}{35},\frac{24\pi}{35}$$ radians.

The trouble is that I have no idea what is meant by "5 parts, which are in A.P.". There is no diagram and the only reference to points A and P I can find is in a much earlier diagram, where AP is an arc subtending an angle of one radian. Does anyone have any ideas, based on the specifications of the problem? Thank you!
A.P. means Arithmetic Progression. In other words, each piece differs from the previous one by a constant amount.

#### Ragnarok

##### Member
Ah, thank you so much! I couldn't imagine what it meant, though it's quite clear now.