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 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)

- 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

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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