Topic Details (Notes format)

How to Use Polar Coordinates in Algebra and Geometry

Subject: Mathematics

Book: Maths Mastery

Polar coordinates (r, θ) describe points by radius (distance from origin) and angle from the positive x-axis. Key conversions with Cartesian are x = r cos(θ), y = r sin(θ). This system simplifies circles, spirals, and rotational symmetries—like expressing conic sections or analyzing waveforms. For instance, a circle of radius a can be written as r = a. Polar coordinates prove handy in advanced geometry, differential equations, and physics (orbital mechanics). Mastery lets you transform complicated Cartesian expressions into more manageable polar forms, expanding your problem-solving toolkit.

Practice Questions

What is the area of a circle with a diameter of 14 cm?

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What is the square root of 121?

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If the average of five consecutive odd numbers is 25, what is the largest number?

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If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

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The area of an equilateral triangle with side length 6 cm is:

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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What is the sum of all odd numbers from 1 to 99?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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