Posted by skye on Thursday, July 26, 2012 at 11:23pm.
given cosŲ = 2/3 and cotŲ > 0
so Ų 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 Ų - √5/3
tanŲ = √5/2
do the second the same way
(Ų will be in quadrant II)
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?
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
cosŲ = -1/3
tanŲ = - 1/2√2 ---> cotŲ = -2√2
I don't know how you possibly got your answers
you have cosŲ = 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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