Find the intersection point of:
Hello, ^_^Engineer_Adam^_^!
Find the intersection point of: .r·cos(θ - ¼π) .= .√2 .and .r·cosθ .= .1
The first curve is: .r·(cosθ·cos¼π + sinθ·sin¼π) .= .√2
. . r·(cosθ·½√2 + sinθ·½√2) .= .√2 . → . r·(cosθ + sinθ) .= .2
. . Then: .r·cosθ + r·sinθ .= .2 . → . x + y .= .2
The second curve is: .r·cosθ .= .1 . → . x = 1
The intersection of the two lines is: .(1, 1)
. . In polar coordinates: .(√2, ¼π)
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If they insist on a general solution:
. . (√2, π/4 + 2kπ) .and .(-√2, 5π/4 + 2kπ) .for any integer k.
Edit: Thanks for the heads-up, Dan. .I fixed my blunder.