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

If the radius of a circle is doubled, what happens to its area?

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The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

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A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

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A cube has a side length of 4 cm. What is its volume?

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

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If 2x = 16, what is the value of x?

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If a = 4 and b = 5, what is the value of (a+b)^2?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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If the sum of three consecutive integers is 72, what are the integers?

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What is the 7th term of the arithmetic progression 3, 6, 9, 12,...?

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