SOLUTION: Use the given information to determine the values of sine 2 theta​, cosine 2 theta​, and tangent 2 theta. sin theta=3/20; The terminal side of theta lies in quadrant I

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Question 1128167: Use the given information to determine the values of sine 2 theta​, cosine 2 theta​, and tangent 2 theta.
sin theta=3/20; The terminal side of theta lies in quadrant II.
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  First, you need to calculate  

        cos%28theta%29 = -sqrt%281-sin%5E2%28theta%29%29 = -sqrt%281-%283%2F20%29%5E2%29 = -sqrt%281-9%2F400%29 = -sqrt%28391%29%2F20.

        Notice that the sign before the final sqrt is " - " ("minus") since the angle theta is in QII.


    Then

        sin%282%2Atheta%29 = 2%2Asin%28theta%29%2Acos%28theta%29 = -2%2A%283%2F20%29%2A%28sqrt%28391%29%2F20%29.


    At this point, I leave it to you to complete, simplify and to get the final number.




2.  Next,  cos%282theta%29 = 1-2%2Asin%5E2%28theta%29 = 1-2%2A%283%2F20%29%5E2.


    Again, at this point, I leave it to you to complete, simplify and to get the final number.




3.  The final step is  tan%282theta%29 = sin%282theta%29%2Fcos%282theta%29,

    which values you substitute from steps 1 and 2.


I completed my instructions.