Question

For what values of x is sin(1/x) = 1

A) x = 0
B) x = π/2
C) x = 1/π
D) x = 2/π

Answer 1

The values of x for which sin(1/x) = 1 are x = 2/π.

Step-by-step explanation:

To find the values of x for which sin(1/x) = 1, we need to solve the equation sin(1/x) = 1 for x.

First, let's find the values of x that satisfy sin(1/x) = 1. Since the range of sin(x) is -1 to 1, only positive values of x will result in sin(1/x) = 1.

We can rewrite the equation as 1/x = sin^-1(1). Using the inverse sine function, we find that sin^-1(1) = π/2. So, 1/x = π/2. Cross-multiplying, we get x = 2/π.

The correct answer is D) x = 2/π.