anonymous
  • anonymous
For right ∆ABC with right ∠C, prove each of the following. a. sin A < 1 b. cos A < 1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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DanJS
  • DanJS
both sin and cos have maximum values at 1, what angles does that occure at for each
anonymous
  • anonymous
um sorry im not to sure
DanJS
  • DanJS

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DanJS
  • DanJS
since the radius is 1, all the hypotenuse are 1, so sin(a) = y and cos(a) = x each point on the circle (x , y) = (cos(a), sin(a))
anonymous
  • anonymous
i have to write a proof
DanJS
  • DanJS
start by stating givens , i havent done a formal one in awhile
DanJS
  • DanJS
try and get through it before doing the formal proof maybe
anonymous
  • anonymous
given sin A< 1
DanJS
  • DanJS
the given triangles are right the sum of the 3 angles in a triangle are 180, so the angles A and B add to 90
DanJS
  • DanJS
the range of values for cos(a) and sin(a), are from -1 to 1 cos(0) = 1 cos(90) = -1, for example
anonymous
  • anonymous
ok
DanJS
  • DanJS
angles A + B + C = 180, and C is said to be 90, so A + B = 90
anonymous
  • anonymous
ok
DanJS
  • DanJS
we are talking about a distance, lengths of the sides, forget about the negative part on the domain of sin and cos, so sin(a) < 1 cos(b) < 1
anonymous
  • anonymous
ok
DanJS
  • DanJS
that restricts all the angles to the first quadrant on that circle, and not including 90, or 0
DanJS
  • DanJS
to prove those, say A+B=90 so angles A and B must both be some value between 0 and 90, not including 0 or 90
anonymous
  • anonymous
ok thanks!!
DanJS
  • DanJS
then apply that to the definition of sin and cos sin(0) = 0 sin(90 = 1 sin has to be less than 1
anonymous
  • anonymous
ok thanks
DanJS
  • DanJS
welcome, i think most of the ideas are there, just organize em,
anonymous
  • anonymous
ok i will thanks so mcuh
DanJS
  • DanJS
overall the remaining unknown angles A and B have to total 90, so A can be 89.99999 and B the rest 0.00001 deg, and that works for example that statement will tell you what the possible values for sin and cos will be
DanJS
  • DanJS
0 < A < 90 0 < B < 90 sin(0) < sin(A) < Sin(90) 0 < sin (A) < 1
DanJS
  • DanJS
sme for cos(A) 0 < A < 90 sin(0) < sin ( A) < sin(90) 0 < sin (A) < 1
DanJS
  • DanJS
the hard part is remembering all the 'official' names for properties and stuff for the reasons

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