University:
University of North Georgia
Course:
MATH 1113 | Precalculus
Academic year:

2024
Views:

97

Pages:

2
Author:

Medonosh0

Pre-Calculus 8.1 - 8.2 Worksheet Name: Assignment: 42 Plot the point that has the given polar coordinates. Label each point! (2, π/2) (-2, -π/3) (3, -2π/3) (1, 0) (-4, π/6) (2, -π/2) (3, 7π/6) (-2, 5π/4) Key: add 2π, add π A point P(r, θ) is given in polar coordinates. Give two other representations of the point, one with r < 0 and one with r > 0. (2, 3π/4) (-2, -π/4), (2, 11π/4) (-2, -π/3) (2, 5π/3), (-2, 7π/3) (-3, 5π/6) (3, 11π/6), (-3, 17π/6) Find the rectangular coordinates for the point whose polar coordinates are given. (6, 2π/3) x = 6cos(2π/3) = -3 y = 6sin(2π/3) = 3√3 (-3, 3√3) (-1, 5π/3) x = -1cos(5π/3) = -1/2 y = -1sin(5π/3) = √3/2 (-1/2, √3/2) (0, 13π) (0, 0) Convert the rectangular coordinates to polar coordinates. (3√3, -3) Q4 r² = (3√3)² + (-3)² = 36 r = 6 tanθ = -3 / 3√3 = -1/√3 θ = -π/6 (6, 11π/6) (-√6, -√2) Q3 r² = (-√6)² + (-√2)² = 8 r = 2√2 tanθ = -√2 / -√6 = 1/√3 θ = π/6 (2√2, 7π/6) (1, -2) Q4 r² = 1² + (-2)² = 5 r = √5 tanθ = -2/1 θ = tan⁻¹(-2) (√5, tan⁻¹(-2)) 17. y = 9 r sin θ = 9 r = 9 csc θ 18. x = y² r cos θ = (r sin θ)² r cos θ = r² sin²θ cos θ = r sin²θ r = cos θ / sin²θ r = cot θ csc θ Convert the polar equation to rectangular coordinates. 19. r = 6 x² + y² = 36 20. r cos θ = 5 x = 5 21. r sin θ = 3 y = 3