Stitz-Zeager_College_Algebra_e-book

# A 117 cos174 117 sin174 116359 12230 3 b 42

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: θ) = 0 −A sin(2θ) + B cos(2θ) + C sin(2θ) = 0 Double Angle Identities From this, we get B cos(2θ) = (A − C ) sin(2θ), and our goal is to solve for θ in terms of the coeﬃcients A, B and C . Since we are assuming B = 0, we can divide both sides of this equation by B . To solve for θ we would like to divide both sides of the equation by sin(2θ), provided of course that we have assurances that sin(2θ) = 0. If sin(2θ) = 0, then we would have B cos(2θ) = 0, and since B = 0, this would force cos(2θ) = 0. Since no angle θ can have both sin(2θ) = 0 and θ) cos(2θ) = 0, we can safely assume sin(2θ) = 0.3 We get cos(2θ) = A−C , or cot(2θ) = A−C . We have B B sin(2 just proved the following theorem. Theorem 11.10. The equation Ax2 + Bxy + Cy 2 + Dx + Ey + F = 0 with B = 0 can be transformed to an equation in variables x and y without any x y terms by rotating the x and y axes counter-clockwise through an angle θ which satisﬁes cot(2θ) = A−C . B We put Theorem 11.10 to good use in the following example. Example 11.6.2. Graph the followin...
View Full Document

## This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online