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

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What is the sum of all angles in a hexagon?

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If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

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

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What is the area of a circle with a diameter of 14 cm?

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A man invests Rs. 5000 at 5% per annum simple interest. What is the total amount after 3 years?

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If 8x = 512, what is the value of x?

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The perimeter of a rectangle is 40 cm, and its length is 12 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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What is the square root of 0.25?

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