Trigonometric Equations and Identities

Professor Mitchell discusses trigonometric equations, covering various types and methods for solving them. The video includes examples of solving equations with single and multiple angles, quadratic forms, and using identities and factoring. It also demonstrates how to use a calculator for solving equations, emphasizing the importance of understanding the unit circle and periodicity of trigonometric functions.

What is a trigonometric equation?

• An equation involving only algebraic expressions

• An equation that contains a trigonometric expression with a variable

• An equation that contains no variables

• An equation that involves only linear functions

What is the first step in solving the equation 5sin(x) = 3sin(x) + √3?

• Divide both sides by sin(x)

• Add 3sin(x) to both sides

• Subtract 3sin(x) from both sides

• Multiply both sides by 2

How do you express the general solution for sin(x) = √3/2?

• x = π/3 + 3nπ, where n is any integer

• x = π/3 + nπ, where n is any integer

• x = π/3 + 2nπ, where n is any integer

• x = π/3 + 4nπ, where n is any integer

What does a multiple angle equation involve?

• No trigonometric functions

• A single trigonometric function

• Multiple trigonometric functions

• A number attached to the variable

What is the solution for tan(2x) = √3 between 0 and 2π?

• x = π/2, 3π/2

• x = π/4, 3π/4

• x = π/6, 5π/6

• x = π/3, 4π/3

How do you solve a trigonometric equation that is quadratic in form?

• By using the sine and cosine rules

• By using the Pythagorean identity

• By using the square root property

• By using the quadratic formula

What is the first step in solving 4cos²(x) - 3 = 0?

• Multiply both sides by 4

• Subtract 3 from both sides

• Divide both sides by 4

• Add 3 to both sides

What should you avoid when solving sin(x)tan(x) = sin(x)?

• Adding sin(x) to both sides

• Subtracting sin(x) from both sides

• Multiplying both sides by sin(x)

• Dividing both sides by sin(x)

What is the zero product principle?

• If a product is zero, neither factor can be zero

• If a product is zero, the product must be negative

• If a product is zero, one of the factors must be zero

• If a product is zero, both factors must be zero

How do you solve an equation using an identity?

• By adding a constant to both sides

• By multiplying both sides by a variable

• By dividing both sides by a constant

• By substituting a known identity