Trigonometric Equation II

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 in the form f(x) = 0, where f(x) includes sine, cosine, tangent, etc.

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 is the period of the sine and cosine functions?

Back

The period of the sine and cosine functions is 2π.

Front

What is the period of the tangent function?

Back

The period of the tangent function is π.

Front

How do you solve the equation 4sin²x = 3?

Back

1. Rewrite as sin²x = 3/4. 2. Take the square root: sinx = ±√(3/4). 3. Find x in the interval [0, 2π) for both positive and negative values.

Front

What are the solutions for sinx = √(3/4) in the interval [0, 2π)?

Back

x = π/3, 2π/3.

Front

What are the solutions for sinx = -√(3/4) in the interval [0, 2π)?

Back

x = 4π/3, 5π/3.

Front

What is the sine addition formula?

Back

sin(a + b) = sin(a)cos(b) + cos(a)sin(b).

Front

What is the cosine addition formula?

Back

cos(a + b) = cos(a)cos(b) - sin(a)sin(b).