MTH 162 Midterm: MTH 162 University of Rochester Exam2Fall 08162 sols

• School: University of Rochester
• Department: Mathematics
• Course: MTH 162
• Professor: All

Document Summary

Part a: (15 points) consider the polar function r( ) = 1 + sin(2 ) (a) sketch the graph of the two-paddled fan on the provided axes. The bounds will be between angles in radian measurement given r = 0. To nd these angles then, we must solve the equation: Therefore, the bounds we will take are 1 = 3 you could have used . Recall that for a polar function, the area is given by. 2 (1 + sin 2 )2 d (c) recall the arc length formula for polar curves is given by s =z 2. The derivative r = 2 cos(2 ), and the bounds are as in part (b). Hint: 1 cos t = 2 sin2( t. 2 ). (c) find the equation of the line tangent to the cycloid at t = . Solution: (a) recall the area under a graph of y is given by.