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

If the length of a rectangle is doubled and the width is halved, what is the change in area?

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If log(100) = 2 and log(10) = 1, what is log(1000)?

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What is the value of log₃(27)?

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If x:y = 2:3 and z:y = 4:3, what is x:z?

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A number is increased by 20% and then decreased by 10%. What is the net change?

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The probability of rolling a sum of 7 with two dice is:

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