Question

Express the polar coordinates (1, - π/6) in Cartesian coordinates. What is the point in rectangular coordinates?

Answer 1

To convert the polar coordinates (1, - π/6) to Cartesian coordinates, apply the formulas x = r ⋅ cos(φ) and y = r ⋅ sin(φ), resulting in the point (sqrt(3)/2, -1/2).

Step-by-step explanation:

The polar coordinates (1, - π/6) can be converted into Cartesian coordinates using the cosine and sine functions. In the polar coordinate system, the first value represents the radius (r), and the second value represents the angle (φ). To convert to Cartesian coordinates (x, y), you can apply the formulas x = r ⋅ cos(φ) and y = r ⋅ sin(φ). Substituting the polar coordinates into these formulas gives:

• x = 1 ⋅ cos(- π/6) = sqrt(3)/2
• y = 1 ⋅ sin(- π/6) = -1/2

Therefore, the Cartesian coordinates corresponding to the polar coordinates (1, - π/6) are (sqrt(3)/2, -1/2).