Q. u=(−5,−8)Find the direction angle of u. Enter your answer as an angle in degrees between 0∘ and 360∘ rounded to the nearest hundredth.θ=□∘
Identify Formula: Identify the formula for the direction angle of a vector. The direction angle θ of a vector u with components (−5,−8) can be found using the arctangent function: θ=arctan(y/x), where x and y are the components of the vector. However, since the vector is in the third quadrant, we need to add 180 degrees to the result of the arctangent to get the angle in the correct range.
Calculate Arctangent: Calculate the arctangent of the y-component divided by the x-component. θ=arctan(xy)=arctan(−5−8)=arctan(58)Using a calculator, we find that arctan(58)≈58.00 degrees.
Adjust for Quadrant: Adjust the angle for the correct quadrant.Since the vector is in the third quadrant, we add 180 degrees to the angle found in Step 2.θ=58.00+180=238.00 degrees
Round Direction Angle: Round the direction angle to the nearest hundredth. θ≈238.00 degrees However, we need to ensure the angle is between 0 and 360 degrees. Since 238.00 is already within this range, no further adjustments are needed.