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.
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.
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