SOLUTION: If tan2theta=3/7 and sec2theta=6, how can I find the exact value of 2theta?

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Question 1002283: If tan2theta=3/7 and sec2theta=6, how can I find the exact value of 2theta?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
tan%282%2Atheta%29=sin%282%2Atheta%29%2Fcos%282%2Atheta%29=3%2F7, can be quadrant 1 or quadrant 3.

sec%282%2Atheta%29=1%2Fcos%282%2Atheta%29=6;
cos%282%2Atheta%29=1%2F6, can mean quadrant 1 or quadrant 4.

2%2Atheta must be in quadrant 1.
2%2Atheta=arccos%281%2F6%29
2%2Atheta=80.4%2Adegrees
highlight%28theta=40.2%2Adegrees%29