ubahlah setiap titik berikut dalam kordinat kutub a. (6,1/4π) b. (3,5π/6) c. (-4,-4) d. (8,15) e. (-5√3,5) mohon bantuannya ya kakak

a dan b ubah jadi koordinat cartesius

a. (6,1/4π)
r = 6
θ = 1/4π = 45°

x = r. cos θ = 6 . cos 45° = 6 x √2/2 = 3√2
y = r. sin θ = 6 . sin 45° = 6 x √2/2 = 3√2

koordinat cartesiusnya (3√2, 3√2)

b. (3,5π/6)
r = 3
θ = 5π/6 = 150°

x = r. cos θ = 3. cos 150° = 3 . -√3/2 = -3√3/2
y = r. sin θ = 3 . sin 150° = 3 . 1/2 = 3/2

koordinat kartesiusnya (-3√3/2, 3/2)

c. (-4,- 4) → kuadran III
x = -4
y = -4

r² = x² + y²
r² = (-4)² + (-4)²
r² = 16 + 16
r² = 32
r = √32
r = 4√2

tan θ  = y/x
tan θ = (-4)/(-4)
tan θ = 1
θ = 225° = 5π/4

koordinat kutubnya (4√2 , 5π/4)

d. (8, 15) → kuadran I

r² = 8² + 15²
r² = (8)² + (15)²
r² = 64 + 225
r² = 289
r = √289
r = 17

tan θ  = y/x
tan θ = 15/8
tan θ = 1,875
θ = 61,93°

koordinat kutub (17, 61,93°)

e. (-5√3, 5) → kuadran II

r² = (-5√3)² + 5²
r² = 75 + 25
r² = 100
r = √100
r = 10

tan θ  = 5/(-5√3)
tan θ = -√3/3
tan θ = 1,875
θ = 150° = 5π/6

koordinat kutub (10, 5π/6)