Posted by skye on Thursday, July 26, 2012 at 11:23pm.
find sin theta and tan theta if cos theta = 2/3 and cot theta is >0
and
find cos theta and cot theta if sin theta = 1/3 and tan theta is <0
thanks! :)

trig  Reiny, Thursday, July 26, 2012 at 11:48pm
given cosØ = 2/3 and cotØ > 0
so Ø must be in quadrant I
make a sketch of a right angled triangle with hypotenuse 3 and adjacent 2
then y^2 + 2^2 = 3^2
y = √5
and sin Ø  √5/3
tanØ = √5/2
do the second the same way
(Ø will be in quadrant II)

trig  skye, Friday, July 27, 2012 at 12:43am
so cos would be root 15/ 4
and cot would be 1/ root 15?
one more question, how do you know it is in the second quadrant?

trig  Reiny, Friday, July 27, 2012 at 8:53am
For the second, draw you triangle in quadrant II
hypotenuse = 3 , opposite = 1
x^2 + 1 = 9
x = ±√8 or ±2√2 , but we are in II, so use x  2√2
cosØ = 1/3
tanØ =  1/2√2 > cotØ = 2√2
I don't know how you possibly got your answers
you have cosØ = 15/4
That would be impossible since the cosine of any angle lies between 1 and +1
I knew the angle was in the second quadrant from the CAST rule. I hope you have been taught that simple pneumonic , it tells you the sign of the 3 main trig functions in each of the 4 quadrants. Do a simple Google search for "CAST rule".
(the sine is positive in I and II,
the tangent is negative in II and IV , so where is the angle ? )
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