Solving trigonometric equations with multiple angles

The video tutorial explains how to solve sine equations, specifically when sine of 2X equals -sqrt(3)/2. It begins by identifying angles on the unit circle where sine equals -sqrt(3)/2, then addresses solving for 2X instead of X. The tutorial continues by finding all solutions using coterminal angles and concludes with the final solution for X.

What is the initial step in solving the equation sin(2X) = -√3/2?

• Find solutions in the interval [0, 4π]

• Find solutions in the interval [π, 2π]

• Find solutions in the interval [0, 2π]

• Find solutions in the interval [0, π]

Which angles on the unit circle have a sine value of -√3/2?

• π/6 and 5π/6

• π/4 and 3π/4

• π/3 and 2π/3

• 4π/3 and 5π/3

What is the significance of coterminal angles in solving trigonometric equations?

• They are irrelevant to the solution

• They help find solutions within a single interval

• They allow for finding multiple solutions by adding or subtracting 2π

• They are used to simplify the equation

How do you find all possible solutions for X in the equation sin(2X) = -√3/2?

• By adding π to each solution

• By subtracting π from each solution

• By dividing the angles by 2 and considering coterminal angles

• By multiplying the angles by 2

What are the final solutions for X in terms of π and a variable N?

• X = π/4 + πN and X = 5π/6 + πN

• X = π/2 + πN and X = 3π/4 + πN

• X = 5π/6 + πN and X = 2π/3 + πN

• X = π/3 + πN and X = 2π/3 + πN