If csc ( x ) = 2 , for 90 ∘ < x < 180 ∘ , then

Question

If  for  

then 

    

 

Answer 1

So we're in quadrant 2, where sine is positive...

csc is 2 which means sin is 1/2

30 degrees causes the sine to be 1/2, so the angle is 150

150 degrees = 150/180*pi = 5*pi/6

squaring this gives 25*pi^2/36

the sine, cosine, and tangent of that angle,

courtesy of MS Excel are,RESPECTIVELY

0.540226833

0.84151944

0.641965957