Steps to Solve Trig Equations

Front

What is the first step in solving trigonometric equations?

Back

Identify the trigonometric function and set the equation to zero.

Front

What does it mean to factor an equation in trigonometry?

Back

To express the equation as a product of its factors, making it easier to solve.

Front

How do you solve the equation 0 = sin(x)(sin(x) - 1)?

Back

Set each factor to zero: sin(x) = 0 or sin(x) - 1 = 0, leading to solutions x = 0, π.

Front

What is the significance of the domain [0, 2π) in trigonometric equations?

Back

It restricts the solutions to the interval from 0 to just below 2π, ensuring all solutions are within one full rotation.

Front

What is the Pythagorean identity in trigonometry?

Back

sin²(x) + cos²(x) = 1.

Front

How do you rearrange the equation 1 - sin²(x) + sin(x) = 1 for factoring?

Back

Move all terms to one side: 0 = sin²(x) - sin(x).

Front

What is the factored form of sec²(x) - sec(x) - 2?

Back

(sec(x) - 2)(sec(x) + 1).

Front

What does tan(x) = 0 imply about the solutions?

Back

The solutions occur at x = nπ, where n is an integer.

Front

What is the relationship between sin²(x) and cos²(x)?

Back

sin²(x) = 1 - cos²(x) (derived from the Pythagorean identity).

Front

What does it mean for a trigonometric function to be undefined?

Back

It occurs when the function's denominator equals zero, such as tan(x) = sin(x)/cos(x) when cos(x) = 0.