If sin(x) = 0, what are the possible values of x?
Correct Answer: x = nπ, where n is any integer
- Step 1: Understand that sin(x) is a function that gives the sine of an angle x.
- Step 2: Know that sin(x) equals 0 at specific angles.
- Step 3: Recall that the sine function is 0 at angles like 0, π, 2π, -π, -2π, etc.
- Step 4: Recognize that these angles can be expressed in a general form as nπ, where n is any integer (like 0, 1, -1, 2, -2, etc.).
- Step 5: Conclude that the possible values of x are all multiples of π.
- Trigonometric Functions – Understanding the properties and values of the sine function, particularly where it equals zero.
- Periodic Functions – Recognizing that sine is a periodic function with a period of 2π, leading to multiple solutions.
- Integer Multiples – Identifying that the solutions involve integer multiples of π.
