anonymous
  • anonymous
Suppose θ is in the interval (180°, 225°). Find the sign of each function value. a) Cos(2θ) b) tan(θ-90°) c) sin(θ/2)
Mathematics
chestercat
  • chestercat
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dumbcow
  • dumbcow
a) 2A puts you in 1st quadrant --> cos(2A) is positive b) A-90 puts you in 2nd quadrant --> tan(A-90) is negative c) A/2 puts you in 2nd quadrant --> sin(A/2) is positive
anonymous
  • anonymous
How do you get to that? Is there any mathmatics behind it that will help me associate it so I can repeat this?
anonymous
  • anonymous
this (rough) diagram should help\ |dw:1328624954731:dw|

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anonymous
  • anonymous
so in first quadrant (0-90) all trig ratios are positive in 2nd (90-180) sine is pos. cos and tan are neg. in 3rd (180-270) tan is pos. sin and cos are neg. in 4th (270-360) cos is pos. sin and tan are neg.
anonymous
  • anonymous
also as an aid to memory you can memorise CAST - 'Cos - All - Sin - Tan' these are the ratios which are positive in the quadrants : |dw:1328625567936:dw| eg 250 degrees - is in third quadrant :- the tangent is positive, cos and sine are negative
anonymous
  • anonymous
hope this helps
anonymous
  • anonymous
Yes this is great information. However, I still don't understand how you find: Suppose θ is in the interval (180°, 225°). Find the sign of each function value. a) Cos(2θ) : What would this be Cos(2*180)? b) tan(θ-90°) c) sin(θ/2)

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