MATH 1172 Midterm: MATH 1172 Ohio State University Math 1172 11.3 Solutions Fa 2014

• School: Ohio State University
• Department: Mathematics
• Course: MATH 1172
• Professor: All

Document Summary

November 4, 2015: find the slope of the line tangent to the curve r = 1 + 2 sin(2 ) at the point (3, /4). Back ground: recall that to nd the slope of a tangent line to an equation in polar coordi- nates, we convert the polar equation to a para- metric equation. Then we use the techniques of parametric equations to nd the derivative of the curve. Recall that we change between polar coordinates and cartesian coordinates through the equations x = r cos y = r sin . Thus if we have a polar function r = f ( ), then we can derive the parametric equation: 7 (cid:0)f ( ) cos , f ( ) sin (cid:1) From here we can nd the slope of the tangent line as a function of . dy dx dy/d dx/d f ( ) cos + f ( ) sin( )