SOLUTION: Given that cotx=-5/6 and x is in quadrant 2, find sin2x, cos2x,tan2x

Algebra ->  Trigonometry-basics -> SOLUTION: Given that cotx=-5/6 and x is in quadrant 2, find sin2x, cos2x,tan2x      Log On


   

Question 992753: Given that cotx=-5/6 and x is in quadrant 2, find sin2x, cos2x,tan2x
Answer by ikleyn(52799) About Me  (Show Source):
You can put this solution on YOUR website!
.
Given that cotx=-5/6 and x is in quadrant 2, find sin2x, cos2x,tan2x
-------------------------------------------------------------------------

cot(x) = -5%2F6     --->     cos%28x%29%2Fsin%28x%29 = -5%2F6 ---> cos%28x%29 = -5%2F6.sin%28x%29     --->

cos%5E2%28x%29 = 25%2F36.sin%5E2%28x%29.         (1)

cos%5E2%28x%29 + sin%5E2%28x%29 = 1,         (2)

Now substitute  (1)  into  (2).  You will get

%281+%2B+%2825%2F36%29%29.sin%5E2%28x%29 = 1,     or

sin%5E2%28x%29 = 36%2F%2825%2B36%29 = 36%2F61.

Hence,   sin(x) = 6%2Fsqrt%2861%29,   cos(x) = -5%2Fsqrt%2861%29     (taking into account that  x  is in the second quadrant).

Now,  when you know  sin(x)  and  cos(x)  values,  you can calculate the remaining functions.

Use the trigonometry formulas

sin(2x) = 2sin(x)*cos(x), = . . . ,

cos(2x) = cos%5E2%28x%29 - sin%5E2%28x%29 = . . . ,

and then  tan(2x) = sin%282x%29%2Fcos%282x%29 = . . . .

Complete these calculations yourself.

Good luck!