Find the smallest positive answer to the equation: sin(2x)=1
I know that sin 90º = 1
so 2x = 90
x = 45º or pi/4 radians
To find the smallest positive answer to the equation sin(2x) = 1, we need to find the value(s) of x that satisfy this equation.
First, let's solve for x in the equation sin(2x) = 1. We know that the sine function has a maximum value of 1, which occurs at x = π/2 + 2πk (where k is an integer).
Therefore, the equation sin(2x) = 1 is satisfied when 2x = π/2 + 2πk. We can solve for x by dividing both sides by 2:
x = (π/2 + 2πk)/2.
We are looking for the smallest positive value of x, so we want to find the smallest value of k that satisfies the equation.
Let's start with k = 0, which gives x = (π/2)/2 = π/4.
Therefore, the smallest positive answer to the equation sin(2x) = 1 is x = π/4.