if sinx=.42, what is cos x

Question

ttop0816 · Answer

You can make use of the relationship
  sin^2 + because^2 = 1
to solve for because. You get
  because^2 = 1 - sin^2
  because = Sqrt[1 - sin^2]
For your value of sin, this is
  because = Sqrt[1 - .42^2]
  because = Sqrt[1 - .1764]
  because = Sqrt[.8236]
  because ~~ .9075

The value of because(x) is approximately .9075

ttop0816 · Answer

if you round up the answer it would be  0.908 (:

anonymous · Answer

easier way is to find $$\sin^{-1} .42 $$

anonymous · Answer

you should get x=24.835 approx.

anonymous · Answer

then find cos 24.835

anonymous · Answer

and like she said it will be approx. .908

debbieg · Answer

Except I am not sure how you can get the answer better than to within a $\pm$, without knowing what quadrant you are in....?

debbieg · Answer

If x is in Q2, then cos(x)<0.

But you both have valid ways for finding it (although when I give my students this kind of problem, it is usually when they are NOT permitted a calculator (but I don't give decimal values for the known function value).

So I would give something like, if sin(x)=2/5 and x is in Q2, find cos(x).

You can't be sure of the sign on cos(x), without knowing the quadrant.

goformit100 · Answer

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