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 sum of three consecutive integers is 96, what are the integers?

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

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What is the length of the diagonal of a square with a side length of 7 cm?

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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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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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

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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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What is the remainder when 5^100 is divided by 3?

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If x - y = 5 and x + y = 15, what is the value of x?

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

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