Trigonometric Identities and Functions

The video tutorial explains how to simplify a conic section equation by rotating the axes. It begins with identifying the problem and the need to eliminate the xy term. The instructor demonstrates how to find the rotation angle using the cotangent formula and trigonometric identities. Conversion equations are derived to express x and y in terms of new variables x' and y'. Finally, the original equation is rewritten and simplified using these new variables, ensuring the xy term is removed.

What is the new expression for X after substitution?

• 3X' + 4Y'

• 4X' + 3Y'

• 4X' - 3Y'

• 3X' - 4Y'

What is the new expression for Y after substitution?

• 4X' - 3Y'

• 3X' + 4Y'

• 3X' - 4Y'

• 4X' + 3Y'

What is the main objective of the given problem?

• To graph the equation

• To solve for X and Y

• To eliminate the XY term by rotating the axes

• To find the roots of the equation

Which formula is used to find the angle of rotation?

• Cosine rule

• Sine rule

• Cotangent 2θ = (A - C) / B

• Tangent rule

What is the simplified form of cotangent 2θ in this problem?

• -7/24

• 7/24

• 24/7

• -24/7

How is the hypotenuse calculated in the triangle used for finding sine and cosine?

• Using the tangent rule

• Using the cosine rule

• Using the sine rule

• Using the Pythagorean theorem

What is the sine of 2θ in this problem?

• -24/25

• -7/25

• 24/25

• 7/25

What is the cosine of 2θ in this problem?

• -24/25

• 24/25

• -7/25

• 7/25

Which identity is used to find the sine of θ?

• Sine double angle identity

• Cosine double angle identity

• Tangent identity

• Half-angle identity

What is the sine of θ calculated using the half-angle identity?

• 5/3

• 4/5

• 5/4

• 3/5