Solving Trig Equations

Front

What is the general form of a trigonometric equation?

Back

A trigonometric equation is an equation that involves trigonometric functions of a variable, typically expressed as f(θ) = 0, where f is a trigonometric function.

Front

What is the sine function?

Back

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

Front

What is the range of the sine function?

Back

The range of the sine function is [-1, 1].

Front

What is the range of the cosine function?

Back

The range of the cosine function is [-1, 1].

Front

What does it mean to solve a trigonometric equation?

Back

To solve a trigonometric equation means to find all angles θ that satisfy the equation within a specified interval.

Front

What is the unit circle?

Back

The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane, used to define trigonometric functions.

Front

How do you find solutions to sin(θ) = k?

Back

To find solutions to sin(θ) = k, use the inverse sine function: θ = arcsin(k) and consider the periodic nature of the sine function.

Front

What is the periodicity of the sine function?

Back

The sine function is periodic with a period of 2π, meaning sin(θ) = sin(θ + 2πn) for any integer n.

Front

What is the periodicity of the cosine function?

Back

The cosine function is periodic with a period of 2π, meaning cos(θ) = cos(θ + 2πn) for any integer n.