Question: Solve the equation sin(3x) = 0 for x in the interval [0, 2π].
Options:
0, π, 2π
0, π/3, 2π/3
0, π/2, π
0, π/4, π/2
Correct Answer: 0, π, 2π
Solution:
The solutions are x = 0, π, 2π, and x = nπ/3 for n = 0, 1, 2, 3, 4, 5.
Solve the equation sin(3x) = 0 for x in the interval [0, 2π].
Practice Questions
Q1
Solve the equation sin(3x) = 0 for x in the interval [0, 2π].
0, π, 2π
0, π/3, 2π/3
0, π/2, π
0, π/4, π/2
Questions & Step-by-Step Solutions
Solve the equation sin(3x) = 0 for x in the interval [0, 2π].
Correct Answer: x = 0, π, 2π, and x = nπ/3 for n = 0, 1, 2, 3, 4, 5.
Step 1: Understand the equation sin(3x) = 0. This means we need to find values of 3x where the sine function equals zero.
Step 2: Recall that sine equals zero at integer multiples of π. So, we can write the equation as 3x = nπ, where n is any integer.
Step 3: Solve for x by dividing both sides of the equation by 3: x = nπ/3.
Step 4: Determine the values of n that keep x within the interval [0, 2π].
Step 5: Calculate the values of x for n = 0, 1, 2, 3, 4, 5: This gives us x = 0, π/3, 2π/3, π, 4π/3, 5π/3, and 2π.
Step 6: List the solutions: x = 0, π, 2π, and x = nπ/3 for n = 0, 1, 2, 3, 4, 5.
Trigonometric Equations – The question tests the ability to solve trigonometric equations, specifically using the sine function and understanding its periodic nature.
Interval Restrictions – The question requires finding solutions within a specified interval, which is crucial for determining valid solutions.
Multiple Solutions – The sine function has multiple solutions within the given interval, and recognizing all possible solutions is essential.
Soulshift Feedback×
On a scale of 0–10, how likely are you to recommend
The Soulshift Academy?
