Topic Details (Notes format)

How to Solve Basic Trigonometric Equations (sin, cos, tan)

Subject: Mathematics

Book: Maths Mastery

Trigonometric equations like sin(x)=√3/2 or cos(x)=–1/2 require knowledge of standard angles and quadrants. For sin(x)=√3/2, principal solutions are x=60° or 120° in the range 0°–180° (or x=π/3 or 2π/3 in radians). Additional solutions repeat every 360° or 2π. Similarly, analyze signs for negative values to find the correct quadrants. These steps let you solve for unknown angles in physics wave problems, geometry angles, or cyclical models. Mastering these equations fosters a deeper ability to interpret sinusoidal relationships in real-world phenomena.

Practice Questions

A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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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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What is the area of an equilateral triangle with side length 10 cm?

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The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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If x^2 + 4x + 4 = 0, what is the value of x?

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

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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What is the value of x if 3x + 7 = 16?

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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