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 sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

View Question

If log(100) = 2 and log(10) = 1, what is log(1000)?

View Question

If sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

View Question

If the length of a rectangle is doubled and the width is halved, what is the change in area?

View Question

If the perimeter of a square is 40 cm, what is the area of the square?

View Question

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

View Question

If x² - 9x + 18 = 0, what are the roots of the equation?

View Question

If 8x = 512, what is the value of x?

View Question

If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

View Question

What is the sum of the first 20 odd numbers?

View Question