SOLUTION: TRIGONOMETRY Write each equation in rectangular-coordinate form 1. r = 1/2+sin๐œƒ 2. r = 6 tan๐œƒsec๐œƒ Show full solution, thank you!

Algebra ->  Test -> SOLUTION: TRIGONOMETRY Write each equation in rectangular-coordinate form 1. r = 1/2+sin๐œƒ 2. r = 6 tan๐œƒsec๐œƒ Show full solution, thank you!       Log On


   

Question 1191547: TRIGONOMETRY
Write each equation in rectangular-coordinate form
1. r = 1/2+sin๐œƒ
2. r = 6 tan๐œƒsec๐œƒ
Show full solution, thank you!


Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
Write each equation in rectangular-coordinate form
1. r+=+1%2F2%2Bsin%28theta+%29

In polar coordinates, x+=+r+%2Acos%28theta+%29 and y=r%2Asin%28theta%29.

=>cos%28theta+%29+=x%2Fr
=>sin%28theta%29=y%2Fr

r+=+1%2F2%2By%2Fr
r+=+%28r%2By%29%2F2r
2r%5E2=r%2By
2r%5E2-r-y=0.....In rectangular coordinates, r=+sqrt%28x+%5E2%2By+%5E2%29

2%28sqrt%28x+%5E2%2By+%5E2%29%29%5E2-sqrt%28x+%5E2%2By+%5E2%29-y=0
โ€‹2%28x+%5E2%2By+%5E2%29-sqrt%28x+%5E2%2By+%5E2%29-y=0
2x+%5E2%2B2y+%5E2-y-sqrt%28x+%5E2%2By+%5E2%29=0


2.
r+=+6+tan%28theta+%29sec%28theta+%29...................tan%28theta+%29=sin%28theta+%29%2Fcos%28theta+%29 and sec%28theta+%29=1%2Fcos%28theta+%29

r+=6%28sin%28theta+%29%2Fcos%28theta+%29%29%281%2Fcos%28theta+%29%29
r+=6sin%28theta+%29%2Fcos%5E2%28theta+%29................cos%28theta+%29=+x%2Fr and sin%28theta+%29=y%2Fr
โ€‹
r+=6%28y%2Fr%29%2F%28x%2Fr%29%5E2
r=%286yr%29%2Fx%5E2
6yr=rx%5E2...........simplify
6y=x%5E2
y=x%5E2%2F6