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 value of log₃(27)?

View Question

If a:b = 3:4 and b:c = 5:6, what is a:c?

View Question

The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

View Question

If 3x = 81, what is the value of x?

View Question

What is the sum of all angles in a hexagon?

View Question

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

View Question

A man spends 75% of his income and saves Rs. 600. What is his total income?

View Question

A man invests Rs. 5000 at 5% per annum simple interest. What is the total amount after 3 years?

View Question

If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

View Question

What is the remainder when 5^100 is divided by 3?

View Question