Answer:
Given that in(theta) = - (2√13)/13 and i is in Quadrant IV, we can determine the value of theta using the inverse trigonometric function arccosine (cos^(-1)).
Since cosine is negative in Quadrant IV, we need to obtain the reference angle from the positive x-axis.
First, let's find the reference angle:
Reference angle = cos^(-1)(|in(theta)|)
Reference angle = cos^(-1)(2√13/13)
Using a calculator, the reference angle is approximately 1.1659 radians.
In Quadrant IV, the angle theta is equal to:
theta = 2π - reference angle
theta ≈ 2π - 1.1659
theta ≈ 4.9767 radians
Now, to find co(2theta), we need to consider that co(2theta) is equal to cosine (2 * theta). Using the calculated value of theta:
co(2theta) = cos(2 * 4.9767)
co(2theta) = cos(9.9534)
co(2theta) ≈ 0.1874
Therefore, co(2theta) is approximately equal to 0.1874.