Sine Function Solutions and Transformations

The video tutorial addresses solving a sine equation with a given domain, focusing on graph transformations and domain modifications. It explains the effects of 2x and pi/3 on the graph, including amplitude changes and horizontal shifts. The instructor demonstrates modifying the domain to align with the equation's argument, solving a simplified version of the equation, and identifying valid solutions within the modified domain. The tutorial concludes with finalizing the solution and verifying it using graph analysis.

What is the main challenge in solving the equation sine(2x + π/3) = 1/2?

• Understanding the horizontal shift and dilation

• Calculating the amplitude

• Identifying the vertical shift

• Finding the period of the sine function

How does the transformation 2x affect the sine graph?

• It stretches the graph vertically

• It increases the amplitude

• It shifts the graph vertically

• It compresses the graph horizontally

What is the purpose of modifying the domain in this problem?

• To match the range of the sine function

• To simplify the equation

• To align with the transformed function

• To eliminate complex numbers

Which angle is a solution to sine(θ) = 1/2 in radians?

• π/4

• π/3

• π/6

• 5π/6

Why is 5π/6 a valid solution in the modified domain?

• It is less than π

• It is greater than 2π

• It fits within the modified domain limits

• It is a common angle for sine

What is the period of the sine function?

• 4π

• 2π

• π

• 3π

How do you find additional solutions for sine(θ) = 1/2?

• By adding π to the initial solution

• By subtracting 2π from the initial solution

• By adding 2π to the initial solution

• By subtracting π from the initial solution

What is the final step in solving the original equation?

• Graphing the function

• Verifying the solutions

• Simplifying the equation

• Checking the domain

Which tool can be used to verify the solutions graphically?

• Calculator

• Desmos

• Excel

• Python

What is the simplified form of 3π/12?

• π/2

• π/6

• π/4

• π/3