Topic Details (Notes format)

How to Graph Trig Functions (Sine, Cosine, Tangent)

Subject: Mathematics

Book: Maths Mastery

Sine and cosine graphs oscillate with amplitude (|A|), period (2π/B), phase shift (C/B), and vertical shift D in y=A sin(Bx–C)+D. For instance, y=2 sin(x–π/2) shifts the standard sin curve right by π/2 and doubles its amplitude. Tangent has vertical asymptotes and repeats every π/B. Graphing these accurately is vital for modeling waves, seasonal cycles, or repeating phenomena. Understanding transformations allows real-life data fitting (harmonic motion, sound waves) and deeper insights into cyclical patterns that shape advanced math or scientific analyses.

Practice Questions

If a cylinder has a radius of 7 cm and height of 10 cm, what is its volume?

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What is the cube root of 729?

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

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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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If a number is divisible by 9, it is also divisible by which of the following?

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What is the sum of the first 10 positive even numbers?

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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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If the perimeter of a square is 40 cm, what is the area of the square?

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A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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

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