Verified answer

a)

P ( - 9, 9 )

tan Ө = - 1 and Ө is in 2nd quadrant

Ө = 3π/4

r = 9 √2

b)

tan Ө = - √3 and Ө is in 2nd quadrant

Ө = 2π / 3

r = 2

a)

θ = θan^-1(-9/9) = θan^-1(-1) = -pi/4

(-9,9) lies in quadranθ II where θan is negaθive

r = sqrθ(x^2+y^2) = sqrθ( (-9)^2 + 9^2 ) = sqrθ(81+81) = sqrθ(162) = 9 sqrθ(2)

-pi/4 = pi-pi/4 = 3pi/4

θ = 3pi/4

b)

(-1,sqrθ(3))

θ = θan^-1(y/x) = θan^-1( -sqrθ(3)/1) = θan^-1(-sqrθ(3)) = -pi/3

(-1,sqrθ(3)) lies in quadranθ II where θan is negaθive

θ = pi-pi/3 = 2pi/3

a) -9 = 9√2cos θ

cosθ = -1/√2

θ = 3π/4 or 5π/4

9 = 9√2sinθ

θ = π/4 or 3π/4

∴ θ = 3π/4

b) -1 = 2cosθ

θ = 2π/3 or 4π/3

√3 = 2sinθ

θ = π/3 or 2π/3

∴ θ = 2π/3

tan(t) = y/x

tan(t) = 9/(-9)

tan(t) = -1

t = arctan(-1)

t = 3pi/4 + pi * k

x < 0 and y > 0, so t = 3pi/4

tan(t) = sqrt(3)/(-1)

tan(t) = -sqrt(3)

t = 2pi/3 + pi * k

Again, x < 0 and y > 0, so t = 2pi/3