To find: a sine and cosine angle and say whether the equation is an ellipse, hyperbola or parabola.
Answer to Problem 29E
The new equation is an ellipse.
The angle is
Sine and cosine angle is,
Explanation of Solution
Given:
Calculation:
Comparing with the standard equation for a quadratic curve,
Thus,
For the cross-product term to vanish, the coordinate axes must be rotated by an angle
Now, using calculator calculate the angle,
And,
After rotation of coordinate axes, the original coordinates,
Substituting the above values of
Simplify.
The equation is an ellipse, having coefficients.
Conclusion:
Hence, the new equation is an ellipse.
The angle is
Sine and cosine angle is
Chapter A5 Solutions
Calculus: Graphical, Numerical, Algebraic
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