Question

Given the polar coordinates r,θ)=(7,5π/4), find the equivalent Cartesian coordinates x,y).

Answer 1

To find the Cartesian coordinates for the polar coordinates (7, 5π/4), we use the equations x = r × cos(θ) and y = r × sin(θ), which give us (-7√2/2, -7√2/2).

Step-by-step explanation:

To convert from polar coordinates to Cartesian coordinates, we use the equations x = r × cos(θ) and y = r × sin(θ). Given the polar coordinates (7, 5π/4), we calculate the Cartesian coordinates as follows:

x = 7 × cos(5π/4) and y = 7 × sin(5π/4)

This specific angle, 5π/4, corresponds to an angle of 225 degrees which is in the third quadrant where both sine and cosine are negative. Thus:

x = 7 × (-√2/2) = -7√2/2
y = 7 × (-√2/2) = -7√2/2

Therefore, the equivalent Cartesian coordinates are (-7√2/2, -7√2/2).