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Basic trignometry function

  1. Jan 27, 2010 #1
    Hi friends,

    Please make me understand this simplest function,

    y = cos θ

    2. in the next step it says: cos θ = sin (π/2 - θ)
    3. and similarly -cos (π/2 - θ) = -sin θ.

    Can anyone please explain how the steps 2 & 3 are deduced.

    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jan 27, 2010 #2
    Do you know what the unit circle is?
  4. Jan 28, 2010 #3


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    Science Advisor

    The most basic definition of "cosine" is that it is "near side divided by hypotenuse" in a right triangle and of "sine" that it is "opposite side divided by hypotenuse".
    Since a right triangle has one angle of size 90 degrees or [itex]\pi/2[/itex] radians, and the angles in any triangle sum to [itex]\pi[/itex] radians, the two acute angles must sum to [itex]\pi- \pi/2= \pi/2[/itex]. That is, if one of the acute angles is [itex]\theta[/itex], then the other is [itex]\pi/2- \theta[/itex]. And, of course, switching angles swaps "near" and "opposite" sides.

    For a more general definition, where [itex]\theta[/itex] is not restricted to be between 0 and [itex]\pi/2[/itex] radians, you would have to go with something like the unit circle definition rochfor1 suggests.
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