More Lessons for Trigonometry

Math Worksheets

In this lesson, we will look at solving Trigonometric Equations.

A trigonometric equation is one that states a relation between trigonometric functions of unknown angles (or numbers)

Trigonometric equations, in general, have an unlimited number of solutions. Usually the domain is restricted to 0 ≤ θ ≤ 360, to limit the number of solutions.

No general method for solving equations can be given. However, the following suggestions will be helpful.

1) Reduce the equation to a simpler equation by factoring, if possible.

2) Simplify the functions of different angles to functions of the same angle by means of known formulas.

3) Simplify the equation so that it involves only the same function of the angle.

4) Check your answers.

**Example:**

Solve

2 cos^{2} *x* = – 3 cos *x* + 2 for *x*, 0° ≤ *x* < 360°

*Solution:*

2 cos^{2} *x* = – 3 cos *x* + 2

2 cos^{2} *x* + 3 cos *x* – 2 = 0

(2 cos *x* – 1)(cos *x* + 2) = 0

2 cos *x* – 1 = 0

*x* = 60°, 300°

or

cos *x* + 2 = 0

cos *x* = –2

*x* = Ø

Therefore, *x* = 60°, 300°

Solve sin 2

sin 2

2 sin

2 sin

sin

sin

or

2 cos

Therefore,

Solving trigonometric equations

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.