Find the cartesian coordinates of the following points given in polar coordinates.
b. (2 rt2, 3pi/4)
I cant figure this one out
I don't know what they call the radius 2 rt2.
Whatever the polar-coordinate radius is, multiply it by cos 3pi/4 to get x and sin 3pi/4 to get y.
cos 3pi/4 = cos 135 degrees = -1/(sqrt 2)
sin 3pi/4 = sin 135 degrees = 1/(sqrt 2)
To convert the given point from polar coordinates to Cartesian coordinates, we can use the following formulas:
x = r * cos(theta)
y = r * sin(theta)
In this case, the given point is (2√2, 3π/4). Let's substitute the values into the formulas:
x = 2√2 * cos(3π/4)
y = 2√2 * sin(3π/4)
To calculate these values, we need to determine the exact values of cosine and sine at 3π/4.
cos(3π/4) = √2/2
sin(3π/4) = √2/2
Substituting these values:
x = 2√2 * (√2/2) = 2
y = 2√2 * (√2/2) = 2
Therefore, the Cartesian coordinates of the point (2√2, 3π/4) are (2, 2).
To find the Cartesian coordinates of a point given in polar coordinates, you can use the following formulas:
x = r * cos(θ)
y = r * sin(θ)
In this case, you are given the polar coordinates of the point as (2√2, 3π/4).
Step 1: Substitute the values into the formulas.
x = (2√2) * cos(3π/4)
y = (2√2) * sin(3π/4)
Step 2: Evaluate the trigonometric functions.
cos(3π/4) = √2/2
sin(3π/4) = √2/2
Step 3: Substitute the values into the formulas.
x = (2√2) * (√2/2) = 2
y = (2√2) * (√2/2) = 2
Therefore, the Cartesian coordinates of the point (2√2, 3π/4) are (2, 2).