The point (-3. -6) lies on the terminal arm of an angle Θ in standard position.
b) Determine the principal angle and the related acute angle.
To find the principal angle, we need to use the inverse tangent function.
The principal angle (Θ) is the angle between the positive x-axis and the line connecting the origin to the point (-3, -6). We can find this angle by taking the arctan of the slope of the line.
The slope of the line is (change in y) / (change in x) = (-6 - 0) / (-3 - 0) = 2.
Taking the arctan of 2 gives us: Θ = arctan(2) ≈ 63.43 degrees.
To find the related acute angle, we use the fact that the acute angle is the absolute value of the principal angle: Θ' = |Θ| = 63.43 degrees.