To find: a sine and cosine angle and say whether the equation is an ellipse, hyperbola or parabola.
Answer to Problem 34E
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,
Hence, the new equation is an ellipse, having coefficients,
Conclusion:
The new equation is an ellipse.
The angle is
Sine and cosine angle is,
Chapter A5 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Precalculus
Calculus & Its Applications (14th Edition)
Calculus: Early Transcendentals (2nd Edition)
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning