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

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

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What is the sum of all even numbers between 1 and 50?

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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What is the value of x if log(x) + log(4) = log(32)?

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What is the HCF of 72 and 120?

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If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

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If x^2 - 5x + 6 = 0, what are the roots?

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