MATH127 Lecture Notes - Lecture 5: Quadratic Equation

• School: University of Waterloo
• Department: Mathematics
• Course: MATH127
• Professor: David Deepwell

Document Summary

From last time . (insert sine graph here) vs (insert inverse sine graph here) d:[-1,1] r:[-pi/2, pi/2] for inverse sine graph. Cos graph vs inverse cos graph ( d: [-1,1] r: [0, pi] for inverse cos graph) Tan vs inverse tan graph (inverse tan graph d: (-infinity, infinity) r: (-pi/2, pi/2) Cos^(theta) + sin^2 (theta) = 1 divide by sin^2(theta) (cos2(theta)/sin^2(theta)) +1 = 1/sin^2(theta) We know that sin theta = opp/hyp, therefore theta= sin^-1(opp/hyp) Ex; evaluate cos theta, sin theta, tan theta, for theta= 25pi/3. Theta = 25pi/3 = 24pi/3 + pi/3 = 8pi + pi/3 = 4(2pi) + pi/3. Cos theta = cos 25pi/3 = cos pi/3 = 1/2. Ex; solve -cos^2 (x) 5/2 sin x + 2 = 0 for o