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(θ) is a function involving sin, cos, tan, etc.

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 cosecant function?

Back

The cosecant function, denoted as csc(θ), is the reciprocal of the sine function, defined as csc(θ) = 1/sin(θ).

Front

What is the range of the sine function?

Back

The range of the sine function is [-1, 1], meaning it can take any value between -1 and 1 inclusive.

Front

What is the range of the cosine function?

Back

The range of the cosine function is also [-1, 1], meaning it can take any value between -1 and 1 inclusive.

Front

How do you solve the equation 4sinθ + 1 = 3?

Back

First, isolate sinθ: 4sinθ = 2, then sinθ = 1/2. The solutions in [0, 2π) are θ = π/6 and θ = 5π/6.

Front

How do you solve the equation 2cscθ + 2 = 0?

Back

First, isolate cscθ: 2cscθ = -2, then cscθ = -1. The solution in [0, 2π) is θ = 3π/2.

Front

What does it mean if a trigonometric equation has no solution?

Back

It means that there are no angles θ in the specified interval that satisfy the equation.

Front

How do you solve the equation 2cosx - 4 = 0?

Back

First, isolate cosx: 2cosx = 4, then cosx = 2. Since the cosine function cannot exceed 1, there is no solution.