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 sum of all even numbers between 1 and 50?

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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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A number is increased by 20% and then decreased by 20%. What is the net change?

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If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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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 all angles in a hexagon?

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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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The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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

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What is the area of a sector of a circle with radius 14 cm and central angle 90°?

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