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.
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.
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.
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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