What is the polar notation for a vector that points from the origin to the point (0,5.00) ?
(5,π/2)
it's right up the y-axis...
r=distance from point to origin
θ=CCW angle from positive x-axis = π/2
So polar notation = (r,θ)=(5, π/2)
To find the polar notation for a vector that points from the origin to a given point in rectangular coordinates, you can use the following steps:
1. Identify the x-coordinate and y-coordinate of the given point.
In this case, the point is (0,5.00), so the x-coordinate is 0 and the y-coordinate is 5.00.
2. Calculate the magnitude (r) of the vector using the Pythagorean theorem.
The magnitude of the vector can be calculated as r = sqrt(x^2 + y^2), where x and y are the respective coordinates.
In this case, the magnitude is r = sqrt(0^2 + 5.00^2) = sqrt(0 + 25.00) = sqrt(25.00) = 5.00.
3. Calculate the angle (θ) of the vector using the inverse tangent function.
Since the point is in the positive y-axis, the angle will be 90 degrees or π/2 radians.
4. Write the polar notation in the form (r, θ).
Combining the magnitude and angle, the polar notation for the vector is (5.00, π/2).
Therefore, the polar notation for a vector that points from the origin to the point (0,5.00) is (5.00, π/2).