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

The LCM of 12 and 15 is:

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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 two complementary angles differ by 30°, what are the angles?

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

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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How many ways can 4 people sit in a row?

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A triangle has angles 60°, 60°, and 60°. What type of triangle is it?

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