Subject: Mathematics
Book: Maths Mastery
To convert (x, y) to polar coordinates (r, θ), use r = √(x² + y²) and θ = tan⁻¹(y/x) (adjusting for quadrant to get correct angles). For example, if x=3, y=3, then r=√18=4.2426..., θ=45°. Conversions unify geometry with trigonometry, letting you interpret points in radial or directional forms. Applications appear in drafting circular motion, analyzing wave patterns, or setting up integrals in advanced calculus. Comfort with conversions fosters deeper 2D geometry insights, bridging rectangular and polar analyses seamlessly.
A number is increased by 20% and then decreased by 20%. What is the net change?
View QuestionWhat is the value of log₃(27)?
View QuestionA cone has a base radius of 7 cm and height of 24 cm. What is its volume?
View QuestionWhat is the cube root of 729?
View QuestionIf the sum of the squares of two consecutive positive integers is 365, what are the integers?
View QuestionIf a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?
View QuestionIf the average of five consecutive odd numbers is 25, what is the largest number?
View QuestionIf x:y = 2:3 and z:y = 4:3, what is x:z?
View QuestionIf a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?
View QuestionIf x^2 + 4x + 4 = 0, what is the value of x?
View Question