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Unformatted text preview: e angle θ = arctan 3 . The
reader is encouraged to think about why there is always at least one acute answer to cot(2θ) = A−C and what this
means geometrically in terms of what we are trying to accomplish by rotating the axes. The reader is also encouraged
to keep a sharp lookout for the angles which satisfy tan(θ) = − 4 in our ﬁnal graph. (Hint: 3 − 4 = −1.)
3 832 Applications of Trigonometry We note that even though the coeﬃcients of x2 and y 2 were both positive numbers in parts 1 and 2
of Example 11.6.2, the graph in part 1 turned out to be a hyperbola and the graph in part 2 worked
out to be a parabola. Whereas in Chapter 7, we could easily pick out which conic section we were
dealing with based on the presence (or absence) of quadratic terms and their coeﬃcients, Example
11.6.2 demonstrates that all bets are oﬀ when it comes to conics with an xy term which require
rotation of axes to put them into a more standard form. Nevertheless, it is possible to determine
which conic section...
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