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

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

a) [�, pi/3] and [�, 5pi/3]
b) [�, pi/6] and [�, 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) (Show Source): You can put this solution on YOUR website!
Start with the given set of equations

Plug in into the first equation

Divide both sides by 2

Take the arcsine of both sides to isolate

Take the arcsine of to get and :

So because the answer format is

this means we have the solutions:

and

So the answer is D)

Note: Since the second equation is , 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)
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