Topic Details (Notes format)

How to Use the Sine, Cosine, and Tangent Functions

Subject: Mathematics

Book: Maths Mastery

Sine (sin), cosine (cos), and tangent (tan) are trigonometric functions relating angles in right triangles to their side lengths. For an angle θ, sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, tan(θ) = opposite/adjacent. These ratios let you find missing angles or sides. For example, if a right triangle has a 30° angle and a hypotenuse of 10, you can use sin(30°) = 1/2 to find the opposite side: (1/2) = opposite/10, so opposite = 5. Trigonometric functions are indispensable in fields like surveying, physics, and engineering, making them a must-learn for geometry applications and practical measurements.

Practice Questions

What is the value of x if log(x) + log(4) = log(32)?

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What is the square root of 121?

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The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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The simple interest on Rs. 4000 at 5% per annum for 2 years is:

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

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A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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

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If sin(θ) = 0.6 and θ is acute, what is cos(θ)?

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

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If a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?

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