sin(pi/5)

a nice trig value with a cool trick

We calculate the value of sin(pi/5) using a clever observation about triangles, the double and triple angle formulas for sin, and the quadratic formula. The result is somewhat reminiscent of the golden ratio and is a must-see for any trigonometry lovers! This is useful for instance in the following video:

[ohanneskamerkoseyan]

I was playing with sin and cos of π/5 a few months ago actually and realized that there's a relation with the golden ratio, namely 2cos(π/5) = φ

[pkvlogs]

Well Dr. Peyam we can calculate the sin(pi/5) by constructing a circle with radius 1 unit and divide the circle into 60 equal parts (each sector contain 6 degree) and join the 0 degree line to 72 degree (2pi /5) their distance would gives u the value of sin(pi/5). lenth of chord if central angle (2theta) is given by 2r sin(theta). so half the length of the chord gives u sin(pi/5) value

[ghstmn]

4:54 cant we also construct a right triagle an dfind sine from there?
Love the video btw

[paulp]

Lovely, But why not (always) use the Po Shen Loh method for quadratic?

[Goldslate]

Hey, Dr. Peyam. Wonderful video. I need some guidance. I have some national level physics exams coming up in February, I've studied a lot but I'm kind of scared to solve questions. I don't like to keep studying, it's also important to apply. I think I'm procrastinating. Do you think there's a fix?

[alipourzand]

sin(3t) = sin(2t) is my favorite trap for students! 😈

[marcelob.]

Dr. Peyam, I'd recommend you do some workout, not much, just enough for health ;-) Brain won't need, you have enough of that.

[joeeeee]

Cos(pi/5) = phi/2
What is sin(pi/5) in terms of phi?