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

What is the greatest common divisor (GCD) of 36 and 48?

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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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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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

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

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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 sum of the interior angles of a hexagon?

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If 2a + b = 10 and a - b = 4, what is the value of a?

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The probability of rolling a sum of 7 with two dice is:

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