Topic Details (Notes format)

How to Use the Pythagorean Identities in Trigonometry

Subject: Mathematics

Book: Maths Mastery

Key Pythagorean trig identities include sin²(θ) + cos²(θ) = 1, 1 + tan²(θ) = sec²(θ), and 1 + cot²(θ) = csc²(θ). These relationships allow you to convert between trigonometric functions or simplify complicated expressions. For example, if sin(θ) = 3/5, then cos(θ) = √(1 – sin²(θ)) = √(1 – 9/25) = √(16/25) = 4/5. This knowledge extends to verifying trigonometric proofs, analyzing wave functions in physics, or building engineering models that rely on sinusoidal behaviors. Familiarity with Pythagorean identities significantly eases advanced problem-solving in calculus and beyond.

Practice Questions

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

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

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If a = 2 and b = 3, what is the value of (a^2 + b^2)?

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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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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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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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What is the LCM of 15 and 20?

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What is the square root of 121?

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The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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