Convert the polar equation θ=3π/4 to a Cartesian equation.

Question

would it be...

a. y=x

b. y=-x

c. y=3pi/4x

d. y=3pi/4

Answer 1

If you draw this, you get a ray emanating from the pole (origin)and headed through the second quadrant. If you consider all possible r values, both positive & negative, then this is a line.  Now you can make the right choice.

Answer 2

θ=3∏/4

at θ=3∏/4, sinθ=√2/2 and cosθ=-√2/2

sinθ/cosθ=(√2/2)/(-√2/2)=-1

sinθ/cosθ=-1

sinθ=-cosθ

x=rcosθ so cosθ=x/r

y=rsinθ so sinθ=y/r

sinθ/cosθ=(y/r)/(x/r)=(y/x)

sinθ/cosθ=-1 from above

therefore (y/x)=-1, or y=-x which is b.