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**

**What is Co-ordinate Geometry?****Rectangular Cartesian Co-ordinates****Polar Co-ordinates****Relation between Cartesian and Polar Co-Ordinates****Distance between Two given Points****Distance between Two Points in Polar Co-ordinates****Division of Line Segment****: Internal & External****Area of the Triangle Formed by Three co-ordinate Points****Condition of Collinearity of Three Points****Medians of a Triangle are Concurrent****Apollonius' Theorem****Quadrilateral form a Parallelogram****Problems on Distance Between Two Points****Area of a Triangle Given 3 Points****Worksheet on Quadrants****Worksheet on Rectangular – Polar Conversion****Worksheet on Line-Segment Joining the Points****Worksheet on Distance Between Two Points****Worksheet on Distance Between the Polar Co-ordinates****Worksheet on Finding Mid-Point****Worksheet on Division of Line-Segment****Worksheet on Centroid of a Triangle****Worksheet on Area of Co-ordinate Triangle****Worksheet on Collinear Triangle****Worksheet on Area of Polygon****Worksheet on Cartesian Triangle**

**11 and 12 Grade Math**** ****From Worksheet on Rectangular – Polar Conversion to HOME PAGE**

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