In math worksheet on rectangular – polar conversion; students can practice the questions on how to convert rectangular coordinates to polar coordinates and also convert polar coordinates to rectangular coordinates (vice-versa).
To convert polar coordinates to rectangular coordinates;
x = r cos θ, y = r sin θ
To convert rectangular coordinates to polar coordinates;
r = √(x² + y²) and tan θ = y/x or, θ = tan\(^{-1}\) y/x
To know more about the relation between the Cartesian co-ordinates and Polar co-ordinates and about more examples Click Here.
Follow the above formula to solve the below questions given in the worksheet on rectangular – polar conversion.
1. OX and OY are the cartesian axes of co-ordinates. Again 0 and OX are respectively the pole and initial line of a system of polar co-ordinates. With respect to these systems (i) if the polar co-ordinates of a point P be (2, 300), find the cartesian co-ordinates of the point; (ii) if the cartesian co-ordinates of a point P be (0, 2), find its polar co-ordinates.
2. Find the Cartesian co-ordinates of the points whose polar co-ordinates are :
(i) (2, π/3)
(ii) (4, 3π/2)
(iii) (6, -π/6)
(iv) (-4, π/3)
(v) (1, √3).
3. Find the polar co-ordinates of the points whose Cartesian co-ordinates are:
(i) (2, 2).
(ii) (- √3, 1)
(iii) (- 1, 1)
(iv) (1, - 1)
(v) (-(5√3)/2, - 5/2).
4. Reduce each of the following Cartesian equations to polar forms:
(i) x² + y² = a²
(ii) y = x tan α
(iii) x cos α + y sin α = p
(iv) y² = 4x + 3
(v) x² - y² = a²
(vi) x² + y² = 2ax
(vii) (x² + y²)² = a²(x² - y²)
5. Transform each of the following polar equations to cartesian forms:
(i) r = 2a sin θ
(ii) l/r = A cos θ + B sin θ
(iii) r= a sin θ
(iv) r² = a²cos 2θ
(v) \(r^{\frac{1}{2}}\) = \(a^{\frac{1}{2}}\) sin θ/2
(vi) r² sin 2θ = 2a²
(vii) r cos (θ - α)
(viii) r(cos 3θ + sin 3θ) = 5k sin θ cos θ.
Answers for the worksheet on rectangular – polar conversion are given below to check the exact answers of the above questions.
1. (i) (√3 ,1)
(ii) (2, π/2);
2. (i) (1, √3)
(ii) (0, -4)
(iii) (3√3, -3)
(iv) (-2, -2√3),
(v) (cos √3, sin √3) where √3 is measured in radian.
3.(i) (2√2, π/4)
(ii) (2, 5π/6)
(iii) (√2, 3π/4)
(iv) (√2, -π/4)
(v) (5, 7π/6)
4. (i) r² = a²
(ii) θ = α
(iii) r cos (θ - α) = P
(iv) r² sin² θ = 4r cos θ + 3
(v) r² cos 2θ = a²
(vi) r = 2a cos θ
(vii) r² = a² cos 2θ.
5. (i) x² + y² = 2ay
(ii) Ax + By = l
(iii) x² + y² = ay
(iv) (x² + y²)² = a²(x² - y²)
(v) (2x² + 2y² + ax)² = a²(x² + y²)
(vi) xy = a²
(vii) x cos α + y sin α = p
(viii) x³ + 3x²y - 3xy²
- y³ = 5kxy.
● Co-ordinate Geometry
11 and 12 Grade Math
From Worksheet on Rectangular – Polar Conversion to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Feb 23, 24 03:55 PM
Feb 23, 24 02:24 PM
Feb 23, 24 01:28 PM
Feb 22, 24 04:15 PM
Feb 22, 24 02:30 PM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.