Answer:
Step-by-step explanation:
Use the conversion formulas to convert from polar coordinates to rectangular coordinates.
x = rcosθ
y = rsinθ
Substitute in the known values of r = 9 and θ = 150 into the formulas.
(9) cos (150)
y = (9) cos (150)
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.
x = 9 (-cos (30))
y = (9) sin (150)
The exact value of cos (30) is √3/2.
x = 9 (-√3/2)
y = (9) sin (150)
Multiply 9 (-√3/2)
x = -9√3/2
y = (9) sin (150)
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
x = -9√3/2
y =9(sin)30
The exact value of sin (30) is ½
x = -9√3/2
y = 9 (½)
Combine 9 and ½
x = -9√3/2
y = 9/2
The rectangular representation of the polar point (9,150) is (−9√3/2, 9/2)
