Trig functions

[DevilSolution]

Im curious to know the relation between sin and cos on a ratio basis. Sin(45) and tan(45) both give approx 0.7071, how do they relate in ratio terms of incremental degree's? The gap decreases? im guessing its something to do with working from 90 as base and then scaling it to 0.1/0.2/0.3 etc as used on a polarized circle graph.

 

The linear ratio would be 1 / 90 * theta;

 

sqrt(2) / 90 * theta gives "close" result upto Sin(45) so the reverse could be used for tan. Is this the right track?

Edited October 9, 2013 by DevilSolution

[studiot]

 

Sin(45) and tan(45) both give approx 0.7071

 

Careful with your figures. Tanx = sinx/cosx.

 

Further angles can be greater than 90 and sin, cos and tan positive or negative.

 

Look here for a table of interest. Post#3 is basic, post#10 more comprehensive.

 

http://www.scienceforums.net/topic/78655-how-do-you-get-the-sine-of-an-angle-without-calculator/

[DevilSolution]

Okay i see, quick switch though, how is sin and tan programmed?

 

Also my formula calculates sin(45) precisely, would it be on the right tracks for a single formula regardless of the angle?

[imatfaal]

Okay i see, quick switch though, how is sin and tan programmed?

 

Also my formula calculates sin(45) precisely, would it be on the right tracks for a single formula regardless of the angle?

 

Programmed - as in calculated within a computer, or calculated in general, or defined?

 

if your formula is theta * sqrt(2)/90 - then no. It works (?) for sin 45 because it collapses to is sqrt(2)/2 which is the same as 1/sqrt(2) which is correct.

 

But you should be able to tell that your formula is not cyclic - it reaches 1 at 63.63 degrees and carries on climbing for ever.

 

I think you can prove that you need a series to approximate Sin Cos and Tan with any accuracy - Studiot will know

[studiot]

 

I think you can prove that you need a series to approximate Sin Cos and Tan with any accuracy - Studiot will know

 

 

It depends what you have already.

 

You can try the identities sin²x+cos²x = 1 and tan²x+1

 

or the multiple angle formule which are also series, but of finite length unlike the infinite series Imatfaal referred to.

 

The simplest of these is sin2x = 2sinxcosx