Final answer:
To find theta in radians given cos(theta) = 0.622, the inverse cosine function, arccos(0.622), is used. The value of theta will be provided in radians directly, typically within the range of 0 to pi, depending on the context of the problem.
Step-by-step explanation:
The student is asking to find the angle theta in radians given that the cosine of theta is 0.622. To find the value of theta in radians, we use the inverse cosine function (also called arccos). We can input the value into a scientific calculator or use software that can perform trigonometric calculations to find:
theta = arccos(0.622)
Depending on the calculator or software, theta will be provided in radians directly. As the cosine function is positive in both the first and fourth quadrants, it's important to consider the context of the question for the correct angle. However, typically the principal value (range from 0 to pi) is given, which would be the answer in this context.