Final answer:
To solve tan(theta) = 1, we find the angle to be 45 degrees (or pi/4 radians), with additional solutions at this angle plus any integer multiple of 180 degrees (or pi radians).
Step-by-step explanation:
The question asks us to solve for tan(theta) = 1. The tangent function equals 1 at specific angles where the sine and cosine functions have the same value because tan(theta) is defined as sin(theta)/cos(theta). The primary angle where this is the case is at theta = 45 degrees (or pi/4 radians) in the first quadrant.
However, since the tangent function is periodic with a period of 180 degrees (or pi radians), we can also add any integer multiple of the period to find additional solutions. Therefore, the general solution will be theta = 45 degrees + n*180 degrees (or theta = pi/4 + n*pi radians), where n is any integer.