Lesson 19 Solving Trigonometric Equations by Factoring

Front

What is a trigonometric equation?

Back

A trigonometric equation is an equation that involves trigonometric functions of a variable, typically an angle, such as sine, cosine, or tangent.

Front

What does it mean to solve a trigonometric equation for \(0 \leq \theta < 2\pi\)?

Back

It means to find all angles \(\theta\) within the interval from 0 to 2π (inclusive of 0 and exclusive of 2π) that satisfy the equation.

Front

What is the first step in solving trigonometric equations by factoring?

Back

The first step is to rearrange the equation into a standard form, typically set to zero, such as \(f(\theta) = 0\).

Front

How do you factor a trigonometric expression?

Back

To factor a trigonometric expression, look for common factors, use identities, or apply techniques similar to factoring polynomials.

Front

What is the zero-product property?

Back

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero.

Front

How do you apply the zero-product property to trigonometric equations?

Back

Set each factor of the equation equal to zero and solve for \(\theta\).

Front

What is the sine function?

Back

The sine function, denoted as \(\sin(\theta)\), is a trigonometric function that relates the angle \(\theta\) to the ratio of the length of the opposite side to the hypotenuse in a right triangle.

Front

What is the cosine function?

Back

The cosine function, denoted as \(\cos(\theta)\), is a trigonometric function that relates the angle \(\theta\) to the ratio of the length of the adjacent side to the hypotenuse in a right triangle.

Front

What is the tangent function?

Back

The tangent function, denoted as \(\tan(\theta)\), is a trigonometric function that relates the angle \(\theta\) to the ratio of the length of the opposite side to the adjacent side in a right triangle.

Front

What are the common angles used in trigonometry?

Back

The common angles are 0, \(\frac{\pi}{6}\), \(\frac{\pi}{4}\), \(\frac{\pi}{3}\), and \(\frac{\pi}{2}\) radians.