# Thread: Finding the intersection point of these:

1. ## Finding the intersection point of these:

Find the intersection point of:

2. Originally Posted by ^_^Engineer_Adam^_^
Find the intersection point of:

Call theta = t for convenience.

The second equation says:
cos(t) = 1/r (For r not equal to 0)

So the first equation says:
r(1/r - pi/4) = sqrt(2)

Now you solve it from here.

-Dan

3. Originally Posted by ^_^Engineer_Adam^_^
Find the intersection point of:

Are you sure that the first equation is not:

r cos(theta -pi/4) =sqrt(2)

RonL

4. Ohhhhh sorry for that ....

Here itis

5. Originally Posted by ^_^Engineer_Adam^_^
Ohhhhh sorry for that ....

Here itis
See here.

-Dan

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)

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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.

7. Originally Posted by Soroban
If they insist on a general solution:

. . (√2, π/4 + 2kπ) .and .(-√2, 3π/4 + 2kπ) .for any integer k.

Ummm...
tan(3*pi/4) = -1, not 1! I think you were thinking of 5*pi/4?

-Dan