Re: Would someone be so kind as to help me with a math equation?

From: Narasimham (mathma18_at_hotmail.com)
Date: 01/01/05 

Date: 1 Jan 2005 10:45:22 -0800

Dark Alchemist wrote:
> I am trying to convert a sin into a cos but all I could come up with
> was the half angle formula which does not give me any negatives. The
> half angle formula has the correct number but it loses the sign.
>
> Formula I tried (simplified) was
>
> x=sin(angle)
> y = sqrt(1 - x^2)
>
> At first I thought I had it because of this
>
> ....Sin.........Cos......Results from the formula above
> -0.95297934 -0.30303527 0.30303528
> -0.95486454 -0.29704159 0.2970416
> -0.95671205 -0.29103617 0.29103617
> -0.95852179 -0.28501927 0.28501926
> -0.96029369 -0.27899111 0.27899109
> -0.96202767 -0.27295194 0.27295194
> -0.96372368 -0.26690199 0.26690199
> -0.96538164 -0.26084151 0.2608415
> -0.96700149 -0.25477073 0.25477072
>
> but when I tested it more I found this
>
> ....Sin.........Cos......Results from the formula above
> 0.05024432 -0.99873696 0.99873696
> 0.04396812 -0.99903293 0.99903293
> 0.03769018 -0.99928947 0.99928947
> 0.03141077 -0.99950656 0.99950656
> 0.0251301 -0.99968419 0.99968419
> 0.01884845 -0.99982235 0.99982235
> 0.01256604 -0.99992104 0.99992104
> 0.00628315 -0.99998026 0.99998026
>
> Notice the digits are correct (within the tolerance of the program I
> used) but I lost their sign. Now the only numbers I know or can
> manipulate is x after the sinewave has been created.
>
> Is there a formula for a full angle as there is for a half angle?
> Thank you.

Resolving a signal to sin/cos components is straight forward. But in
the opposite direction,trying to find cos from sin or vice versa
entails dealing with two sign possibilities in each quadrant. All
Silver Tea Cups (All,Sin,Tan,Cos) rule helps find correct sign of sin
and cos in each quadrant. Draw a graph of sin and cos (angle 0 to 2 Pi)
and see which quadrants give sin / cos positive or negative, write
small program to decide sign depending on Int[angle/(pi/2)]+1 = n.

Relevant Pages

  • Re: The prosthapheresis formulae
    ... sin(a + b) = sin a cos b + cos a sin b ... standard circle with centre O. Later the chord function was replaced by ... the modern sine (half the chord of twice the angle), ...
    (sci.math)
  • Re: Sin Cos Tan, why not Sin Sec Tan?
    ... there's a symmetry between the two ... >> functions it should become clear to you that sin and cos are a natural ... >> pair, whereas the relationship between sin and sec, for example, is more ... Use complimentary angles: the compliment of an angle, co-angle, is a ...
    (sci.math)
  • Re: Sin Cos Tan, why not Sin Sec Tan?
    ... >>I can see how sin and cos are a natural pair, ... >>cofunction of sin. ... >>(sin and its cofunction, cos) and. ... > right angle minus the original angle, which for either acute angle in a ...
    (sci.math)
  • Re: S - Y Parameter conversion with Smith Chart
    ... f71@4ax.com>) about 'S - Y Parameter conversion with Smith Chart', ... Be careful of the signs of sin and cos if angle is negative. ...
    (sci.electronics.design)
  • Re: Would someone be so kind as to help me with a math equation?
    ... >I am trying to convert a sin into a cos but all I could come up with ... > was the half angle formula which does not give me any negatives. ... Some reason you don't just use the inverse trig function for sin? ... Brian ...
    (sci.math)