Question

PLEASE HELPPP!!!!
13. Find the rectangular coordinates of (9, 150°).
(Show work)

Answer 1

The rectangular representation of the polar point (9,150) is (−9√3/2, 9/2)

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)

Answer 2

Explanation:

Substitute in the known values of

r = 9 and θ =150 into the formulas. (9) cos (150)

y = (9) sin (150)

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)

blah blah blah

(9, 150) is

`( - (9 √(3) )/(3) \: \: (9)/(2) )`