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

A car travels 240 km in 4 hours. What is its average speed?

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A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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If 2x = 16, what is the value of x?

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

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If sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

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A sphere has a radius of 7 cm. What is its volume?

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The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

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What is the LCM of 15 and 20?

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