SOLUTION: #10 Find the coordinates [r, theta] of all points of intersection: r = 2sin(theta) and r = 1 a) [½, pi/3] and [½, 5pi/3] b) [½, pi/6] and [½

Algebra ->  Trigonometry-basics -> SOLUTION: #10 Find the coordinates [r, theta] of all points of intersection: r = 2sin(theta) and r = 1 a) [½, pi/3] and [½, 5pi/3] b) [½, pi/6] and [½      Log On


   

Question 122078: #10
Find the coordinates [r, theta] of all points of intersection:
r = 2sin(theta) and r = 1

a) [½, pi/3] and [½, 5pi/3]
b) [½, pi/6] and [½, 5pi/6]
c) [1, pi/3] and [1, 5pi/3]
d) [1, pi/6] and [1, 5pi/6]
e) None of these
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given set of equations







Plug in r=1 into the first equation




Divide both sides by 2



Take the arcsine of both sides to isolate



or Take the arcsine of 1%2F2 to get pi%2F6 and 5pi%2F6:






So because the answer format is this means we have the solutions:


and


So the answer is D)


Note: Since the second equation is r=1, this means that the first coordinate (which is r) is also 1. So the answers will look like (1,?) and (1,?). So if you had no idea what to do, you could easily eliminate possible answers a) and b)