Final answer:
For cos(θ)=0.7071, θ is most commonly 45° or 315° in degrees, which are equivalent to π/4 and 7π/4 radians respectively.
Step-by-step explanation:
If cos(θ)=0.7071, then θ corresponds to an angle whose cosine is equal to 1/√2 or √2/2 because 0.7071 is approximately the decimal expansion of 1/√2. This value is associated with an angle of 45° for θ in the first quadrant. However, cosine is also positive in the fourth quadrant, so θ could also be 315° (or equivalently, -45°). These answers are specific to angles in the range of 0° to 360°. When discussing the unit circle or trigonometric functions in radians, these angles are π/4 and 7π/4 radians, respectively.
In the context of the question details, confusion seems to arise from the symbolic or mathematical expressions provided, which are not directly relevant to solving the question at hand. However, recognizing that cosine values can repeat in different quadrants is important for considering all possible solutions.