1. Find the polar coordinates of (8, –8) for r > 0.
2.Find the rectangular coordinates of (9, 150°)
(r,θ) = (8√2,315°) or ((8√2,-45°)
(x,y) = (9cos150°,9sin150°) = (-9/2, 9/2 √3)
dang - gotta stop typing too fast:
(x,y) = (9cos150°,9sin150°) = (-9/2 √3, 9/2)
To find the polar coordinates of a point (x, y), you can use the following formulas:
1. For r > 0:
- r = √(x^2 + y^2) (distance from the origin to the point)
- θ = arctan(y/x) (angle between the positive x-axis and the line connecting the origin and the point)
Now let's apply these formulas to the given points:
1. For (8, -8):
- Using the formula r = √(x^2 + y^2), we calculate:
r = √(8^2 + (-8)^2) = √(64 + 64) = √128 ≈ 11.31 (rounded to two decimal places)
- Using the formula θ = arctan(y/x), we calculate:
θ = arctan((-8)/8) = arctan(-1) ≈ -45° (rounded to the nearest degree)
Therefore, the polar coordinates for (8, -8) when r > 0 are approximately (11.31, -45°).
2. For (9, 150°):
- The given point is already in polar form, where 9 represents the value of r and 150° represents the value of θ.
Therefore, the rectangular coordinates for (9, 150°) are (9 * cos(150°), 9 * sin(150°)).
Evaluating this, we have:
x = 9 * cos(150°) ≈ -4.5
y = 9 * sin(150°) ≈ 7.79
Thus, the rectangular coordinates for (9, 150°) are approximately (-4.5, 7.79).