Question

how do you get the value of sin35(degrees) MANUALLY?

Answer 1

by luckily finding 2 angles that you know of that will add or subtract to it

Answer 2

sin(60-45)

Answer 3

sin(a+b) = sin(a)cos(b)+sin(a)cos(b)

Answer 4

thing is 60-45 not= 35 :)

Answer 5

I think that is is equal to sin(20 +15) an I know how to solve for sin 15.but how do I get the value of sin20? O_O

Answer 6

sin(60-45) =sin60cos45+sin45cos60

Answer 7

60-45 is never 35 :)

Answer 8

oh yes.. my mistake :) maybe sin(30 + 30/6)? = sin30cos30/6 + cos30sin30/6 but it involves a lot of theorems

Answer 9

In the old days, you would get out a quill pen and start figuring...

with x in radians, this has a relative error of less than 1.9%
\[ sin(x) =\frac{16x(\pi-x)}{5\pi^{2}-4x(\pi-x)} \]

See
http://en.wikipedia.org/wiki/History_of_trigonometry
Indian Mathematics

Or use Newton's series definition

(again, x in radians)
\[ sin(x)= x - \frac{x^{3}}{3!} + \frac{x^{5}}{5!} - \frac{x^{7}}{7!} + …\]


Test:
sin(35)= 0.573576436 by a Casio calculator


with pi= 3.141592654
x= 35*pi/180= 0.610865238 radians (tedious if done by hand, but doable)

Using formula (1)
16*0.610865238*(pi-0.610865238)/(5*pi*pi-4*0.610865238*(pi-0.610865238)
= 0.573041637

Using 4 terms of Newton's series
0.610865238-0.610865238^3/6 + 0.610865238^5/120-0.610865238^7/5040
=0.573576404

Using 5 terms:
0.573576404+0.610865238^9/362880
=0.573576437