If we draw v and w with the same initial point we

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Unformatted text preview: e angle θ = arctan 3 . The 4 4 reader is encouraged to think about why there is always at least one acute answer to cot(2θ) = A−C and what this B 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 4 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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