Convert theta = pi/4 to rectangular equation
you need both a radius and an angle to convert from polar to x,y coordinates
x = r cos theta
y = r sin theta
if you mean radius of 1 (unit vector
then
x = 1 cos pi/4
y = 1 sin pi/4
since cos pi/4 = sin pi/4 = sqrt 2 /2
x = 1 sqrt 2 /2
and
y = sqrt 2 /2
Thank you
To convert theta = pi/4 to a rectangular equation, we can use the following relationships:
x = r * cos(theta)
y = r * sin(theta)
In this case, we are given theta = pi/4. Let's assume r = 1 for simplicity.
Substituting these values into the equations:
x = 1 * cos(pi/4)
y = 1 * sin(pi/4)
Simplifying further:
x = sqrt(2)/2
y = sqrt(2)/2
Therefore, the rectangular equation is:
(x, y) = (sqrt(2)/2, sqrt(2)/2)
To convert the polar equation θ = π/4 to a rectangular equation, we can use the formulas:
x = r * cos(θ)
y = r * sin(θ)
In this case, since we only have θ and no value for r, we can assume that r is a positive constant. Let's assume r = 1 for simplicity.
Using the formulas, we have:
x = 1 * cos(π/4)
y = 1 * sin(π/4)
Evaluating the trigonometric functions, we get:
x = (√2)/2
y = (√2)/2
Therefore, the rectangular coordinates for the polar equation θ = π/4 are x = (√2)/2 and y = (√2)/2.