Find two values of 0, 0 ≤ 0 ≤ 2π that satisfy the following equation. Show your work.
tan 0 = 1
The tangent function has a period of π, which means that the values of the tangent function repeat every π units.
Since we are looking for values between 0 and 2π, we can add any multiple of π to find different values that satisfy the equation.
To find the value of 0 where tan 0 = 1:
We know that tan 0 = 1 corresponds to one of the special angles in the unit circle, which is π/4 or 45 degrees.
So, the first value of 0 that satisfies the equation is π/4 or 45 degrees.
To find another value within the given range, we can add the period of the tangent function, which is π, to the first value:
π/4 + π = 5π/4
So, the second value of 0 that satisfies the equation is 5π/4 or 225 degrees.