SOLUTION: Let tan theta = 5/12 with theta in QI Find Sec 2 theta -------- This chapter is on Double angle formulas. I do not know how to set up the equation for sec or csc.

Question 956870: Let tan theta = 5/12 with theta in QI Find Sec 2 theta -------- This chapter is on Double angle formulas. I do not know how to set up the equation for sec or csc.
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Let tan theta = 5/12 with theta in QI Find Sec 2 theta -------- This chapter is on Double angle formulas. I do not know how to set up the equation for sec or csc.
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Working with a (5-12/13) reference right triangle in quadrant I
tan theta=5/12=sin theta/cos theta
cos theta=12/13
sin theta=5/13
cos 2 theta=cos^2 theta-sin^2 theta=144/169-25/169=119/169
sec 2 theta=1/cos 2 theta
sec 2 theta=169/119
..
Check w/calculator:
tan theta=5/12
theta≈22.52
2theta≈45.24
cos 2 theta=cos(45.24)≈0.7041
exact value=119/169≈0.7041
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