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

Front

What is the solution set for a trigonometric equation over the interval [0, 2π)?

Back

The solution set consists of all angles within the interval [0, 2π) that satisfy the equation.

Front

How do you find solutions to sin(x) = 0.5 in the interval [0, 2π)?

Back

The solutions are x = π/6 and x = 5π/6.

Front

What are the solutions to cos(x) = 0 in the interval [0, 2π)?

Back

The solutions are x = π/2 and x = 3π/2.

Front

What is the significance of the unit circle in solving trigonometric equations?

Back

The unit circle helps visualize the values of sine and cosine for different angles, aiding in finding solutions to trigonometric equations.

Front

What is the periodicity of sine and cosine functions?

Back

The sine and cosine functions are periodic with a period of 2π, meaning their values repeat every 2π radians.

Front

How do you express the general solution for sin(x) = 0.5?

Back

The general solution is x = π/6 + 2πn and x = 5π/6 + 2πn, where n is any integer.

Front

What are the solutions to tan(x) = 1 in the interval [0, 2π)?

Back

The solutions are x = π/4 and x = 5π/4.

Front

How do you solve a trigonometric equation involving multiple angles, such as sin(2x) = 0?

Back

You can use the double angle identity and solve for x by finding the angles where sin(x) = 0.

Front

What is the relationship between sine and cosine in a right triangle?

Back

In a right triangle, sine is the ratio of the length of the opposite side to the hypotenuse, while cosine is the ratio of the length of the adjacent side to the hypotenuse.