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 x:y = 2:3 and z:y = 4:3, what is x:z?

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If the perimeter of a square is 36 cm, what is the length of its diagonal?

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

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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 sum of the interior angles of a hexagon?

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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 slope of a line passing through the points (2, 3) and (4, 7)?

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If the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

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

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