SOLUTION: TRIGONOMETRY Write each equation in polar-coordinate form 1. 𝑥²+(y-5)²=25 2. 5x - 2y=1 Show full solution, thank you!

Algebra ->  Test -> SOLUTION: TRIGONOMETRY Write each equation in polar-coordinate form 1. 𝑥²+(y-5)²=25 2. 5x - 2y=1 Show full solution, thank you!      Log On


   

Question 1191548: TRIGONOMETRY
Write each equation in polar-coordinate form
1. 𝑥²+(y-5)²=25
2. 5x - 2y=1
Show full solution, thank you!
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

1. x%5E2%2B%28y-5%29%5E2=25

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

Thus, the input can be rewritten as

%28r+%2Acos%28theta+%29%29%5E2%2B%28r%2Asin%28theta%29-5%29%5E2=25

r%5E2+%2Acos%5E2%28theta+%29%2Br%5E2%2Asin%5E2%28theta%29-2%2A5r%2Asin%28theta%29%2B25=25

r%5E2+%28cos%5E2%28theta+%29%2Bsin%5E2%28theta%29%29-10r%2Asin%28theta%29=25-25

r%5E2+%281%29-10r%2Asin%28theta%29=0

r%5E2=10r%2Asin%28theta%29

r=10sin%28theta%29


2.

5x+-+2y=1

x+=+r+%2Acos%28theta+%29+and y=r%2Asin%28theta%29

5r+%2Acos%28theta+%29++-+2r%2Asin%28theta%29=1

r+%285cos%28theta+%29++-+2sin%28theta%29%29=1

r+=1%2F%285cos%28theta+%29++-+2sin%28theta%29%29