SOLUTION: Find an equivalent equation in rectangular coordinates. r(cos θ - sin θ) = 5

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Question 1043550: Find an equivalent equation in rectangular coordinates.
r(cos θ - sin θ) = 5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We'll use these identities
Identity 1: x+=+r%2Acos%28theta%29
Identity 2: y+=+r%2Asin%28theta%29


r%2A%28cos%28theta%29+-+sin%28theta%29%29+=+5 Original equation


r%2Acos%28theta%29+-+r%2Asin%28theta%29+=+5 Distribute the 'r' through


x+-+r%2Asin%28theta%29+=+5 Use identity #1 (see above)


x+-+y+=+5 Use identity #2 (see above)


So r%2A%28cos%28theta%29+-+sin%28theta%29%29+=+5 transforms into x+-+y+=+5 which is in rectangular form. This is a linear equation in standard form. If you wish to convert to slope intercept form, then solve for y to get


x+-+y+=+5


x+-+y%2By+=+5%2By Add y to both sides


x+=+5%2By


y%2B5+=+x


y%2B5-5+=+x-5 Subtract 5 from both sides


y+=+x-5


So x+-+y+=+5 is equivalent to y+=+x-5

Depending on how your teacher wants the answer, the final answer is either x+-+y+=+5 or it is y+=+x-5