3.Find the area of the region bounded by the parametric curve and the x-axis. (10 pts) = 6 (0- sin 0) y=6(1 - cos 0) 0<02T Find the slope of the tangent line at the given point. (10 pts) 4. r 2+sin 30, 0=T/4
1. Find the area of the region bounded by the parametric curve x = 2 sin? t and y= 2 sin? t tan t on the interval 0 <t< . Show your work. 2. Determine whether the following statement is true or false: Ify is a function oft and x is a function of t, then y is a function of x. If the statement is false, explain (in 2-4 complete sentences) why or give an example that shows it...
Find the area of the region bounded by the curves r = 2 + cos(2), 0 = 0, and = /4. You may need the formulas: cos” (a) = 1+ cos(22), sin?(x) = 1 – cos(22)
296. Area under a curve. The area of the region bounded by the curve y = (-2<x< 2), the x-axis, V4 - x4 V4- and the lines x = a and x = b(a < b) is given by sin - €) - sin-"). a. Find the exact area if a 1 and 1 b. Find the exact area if a = -V3 and 5 = vā.
Find the area of the right half of the cardioid: r = 4+3 sin 0. Find the area enclosed within one loop of the curve: r = 4 cos 30.
3 Given sin osesan and sin B -7 37 25 <B< 27. Find cos(0 + B).
rose 3 sin (40) - Find all points 0 <0 < 27 where the curve r = 2 - 4 cos 0 has vertical or horizontal unes.
show all work please (5 pts) Find the area of the region bounded by the graphs of y + 2 and y = [ +1,0 < x < 2. 2 Sketch the region.
Use a double integral to find the area of the region bounded by the cardioid r= -2(1 - cos 6). Set up the double integral as efficiently as possible, in polar coordinates, that is used to find the area. r drdo (Type exact answers, using a as needed.)
Find all solutions to cos(7a) - cos(a) = sin(4a) on 0 Sa<