# Unit circle problem

#### naeimuon

Hello guys, so I have this problem in my assignment that I just can't seem to understand and answer - hope you guess are able to help, thank you.

a) In the diagram, radii drawn to endpoints of a chord of the unit circle determine a central angle a. Show that the length of the chord is L = sqrt(2-2cos(Ø))

b) By using the substitution Ø = a/2 in the double angle formula cos2Ø = 1-2 sin^2 Ø, derive a formula for sin a/2, that is a half-angle formula for the sine function.

c) Use the result in (a) and your result in (b) to show that the length of the chord is L = 2 sin(Ø/2)

#### Cervesa

Last edited:
• topsquark

#### Plato

MHF Helper
Hello guys, so I have this problem in my assignment that I just can't seem to understand and answer - hope you guess are able to help, thank you.

a) In the diagram, radii drawn to endpoints of a chord of the unit circle determine a central angle a. Show that the length of the chord is L = sqrt(2-2cos(Ø))

b) By using the substitution Ø = a/2 in the double angle formula cos2Ø = 1-2 sin^2 Ø, derive a formula for sin a/2, that is a half-angle formula for the sine function.

c) Use the result in (a) and your result in (b) to show that the length of the chord is L = 2 sin(Ø/2)
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