Finding Trig Ratios of Any Angle: A General & Easy Way

[The legend]

Is there any general and hopefully 'easy' way to find the trigonometric ratios of any angle? That is without using the sin, cos etc tables?

If not any angle ... atleast whole number angles?

 

[danago]

Do you mean also without a calculator?

If so, then the 'easiest' way that i can think of is to draw a unit circle on an x-y plane, use a protractor to draw a radius at the specific angle from the +x axis and then measure the x (cosine) and y (sine) coordinates of the point. Won't be the most accurate answer though, but it should be roughly around the correct value.

You could also use a Taylor expansion approximation and just take the first few terms?

Or else just use a calculator? Cant be easier than this :P

 

[Feldoh]

You can use the double angle identities and usually derive any angle just using the typical angles memorized using the unit circle.

 

[The legend]

yes, i did mean without a calc...
by the way what's this Taylor expansion approximation and how can i use it?
I did try googling but well didn't understand it.

The circle method is good though...

 

[The legend]

You can use the double angle identities and usually derive any angle just using the typical angles memorized using the unit circle.

hey i forgot that!
But nice idea!

The double and triple angle identities would be angels!

 

[The legend]

Another wonderful thing
http://mathforum.org/library/drmath/view/64635.htmlhttp://en.wikipedia.org/wiki/CORDIC

 

[The legend]

A series for a good approximation of all trig values(time consuming though)

http://en.wikipedia.org/wiki/Trigonometric_function#Series_definitions

(found 'em by googling and seeing wikipedia...never knew they were such good info givers)

 

[Feldoh]

A series for a good approximation of all trig values(time consuming though)

http://en.wikipedia.org/wiki/Trigonometric_function#Series_definitions

(found 'em by googling and seeing wikipedia...never knew they were such good info givers)

If you going to try Taylor expansion's you don't want to use those expansions. Those series converge very slowly to the correct values. You could probably find a faster approximation somewhere.