Rotating Conic Sections and Angles

The video tutorial explains the concept of rotating conic sections, focusing on how to handle equations with an XY term. It covers finding the angle of rotation using a specific formula and substituting X and Y to eliminate the XY term. The tutorial includes example problems, demonstrating the process of rewriting equations in terms of new axes and graphing the resulting conic sections. The video emphasizes understanding the transformation of coordinates and the characteristics of the resulting conic sections.

Why is the rotation of conics necessary when dealing with equations containing an XY term?

• To change the type of conic section.

• To increase the complexity of the equation.

• To make the graph parallel to the X or Y axis.

• To simplify the equation by removing the XY term.

What is the formula used to find the angle of rotation for a conic section?

• tangent of theta equals a minus B over C

• sine of theta equals a plus C over B

• cosine of two theta equals B over a minus C

• cotangent of two theta equals a minus C over B

In the example problem, what is the angle of rotation found for the equation XY - 1 = 0?

• PI over 3

• PI over 6

• PI over 4

• PI over 2

When graphing a rotated conic, what is the new axis called?

• X'Y' axis

• Rotated axis

• XY axis

• Prime axis

In the practice problem, what type of conic section is identified after rotation?

• Ellipse

• Parabola

• Hyperbola

• Circle

What is the angle of rotation for the horizontal ellipse example?

• PI over 2

• PI over 3

• PI over 6

• PI over 4

In the final example, what method is used to find exact trigonometric values for the angle of rotation?

• Reciprocal identities

• Pythagorean theorem

• Half-angle formulas

• Unit circle