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**Unformatted text preview: **he following example.
1 Sound familiar? In Section 11.4, the equations x = r cos(θ) and y = r sin(θ) make it easy to convert points
from polar coordinates into rectangular coordinates, and they make it easy to convert equations from rectangular
coordinates into polar coordinates.
2
We could, of course, interchange the roles of x and x , y and y and replace φ with −φ to get x and y in terms
of x and y , but that seems like cheating. The matrix A introduced here is revisited in the Exercises. 828 Applications of Trigonometry Example 11.6.1. Suppose the x and y axes are both rotated counter-clockwise through an angle
θ = π to produce the x and y axes, respectively.
3
1. Let P (x, y ) = (2, −4) and ﬁnd P (x , y ). Check your answer algebraically and graphically.
√
2. Convert the equation 21x2 + 10xy 3 + 31y 2 = 144 to an equation in x and y and graph.
Solution.
1. If P (x, y ) = (2, −4) then x = 2 and y = −4. Using these values for x and y along with
θ = π , Theorem 11.9 gives x = x cos(θ) + y sin(θ) = 2 cos π + (−4) sin π which s...

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