Question

Finding Sin(55°)
I found that Sin(55°) = Sin(11Pi /36) ?
Help please, without using the calculator!!

Answer 1

you can try this

you know that sin 45 is sqrt(2)/2 and sin(60) is sqrt(3)/2

sin(55) is between them

The closer to 55 the better so, we weight by the inverse of the distance between these angles

we'll give the sin 45 a weight of 1/(55-45) = 1/10 and sin 60 a weight of 1/(60-55) = 1/5 -- this is larger because 60 is closer to 55 than 45.

So, cos(55) is about ((1/10)*sin 45 + (1/5)*sin(60)) / ( 1/10 + 1/5)

Using this technique will get you to the exact value of 1% (without a calculator - or calculus).

If you know calculus, you can use the taylor expansion of cos(x), which will be as accurate as you want:

sin(x) = x-x^3/6+x^5/120-x^7/5040+x^9/362880-x^11/39916800+O(x^12)

Answer 2

Thank you so much :)

Answer 3

NP

A couple of typos -

*So, sin(55) is about ((1/10)*sin 45 + (1/5)*sin(60)) / ( 1/10 + 1/5)

*If you know calculus, you can use the taylor expansion of sin(x), which will be as accurate as you want:

sin(x) = x-x^3/6+x^5/120-x^7/5040+x^9/362880-x^11/39916800+O(x^12)