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Which of the following is the direction angle of w=1-61 ? Round your answer to the nearest hundredth of a degree. O 67.38° 112.62° 247.38° 292.62°

Which of the following is the direction angle of w=1-61 ? Round your answer to the nearest hundredth of a degree. O 67.38° 112.62° 247.38° 292.62°

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Direction Angle Calculation Question #### Problem Statement: Which of the following is the direction angle of \( w = \frac{5}{2} - 6i \)? Round your answer to the nearest hundredth of a degree. #### Answer Choices: - \( A. \) \( 67.38^\circ \) - \( B. \) \( 112.62^\circ \) - \( C. \) \( 247.38^\circ \) - \( D. \) \( 292.62^\circ \) #### Instructions: Choose the correct direction angle from the options provided above. Note that the direction angle should be calculated and rounded to the nearest hundredth of a degree. #### Explanation: To solve for the direction angle of a complex number \( w \) of the form \( a + bi \), the formula used is \( \theta = \tan^{-1}\left(\frac{b}{a}\right) \). The angle may need to be adjusted based on the quadrant in which the complex number is located. In this case, \( w = \frac{5}{2} - 6i \), where \( a = \frac{5}{2} \) and \( b = -6 \). Calculate the direction angle using the arctangent function and adjust based on the quadrant if necessary.
Transcribed Image Text:### Direction Angle Calculation Question #### Problem Statement: Which of the following is the direction angle of \( w = \frac{5}{2} - 6i \)? Round your answer to the nearest hundredth of a degree. #### Answer Choices: - \( A. \) \( 67.38^\circ \) - \( B. \) \( 112.62^\circ \) - \( C. \) \( 247.38^\circ \) - \( D. \) \( 292.62^\circ \) #### Instructions: Choose the correct direction angle from the options provided above. Note that the direction angle should be calculated and rounded to the nearest hundredth of a degree. #### Explanation: To solve for the direction angle of a complex number \( w \) of the form \( a + bi \), the formula used is \( \theta = \tan^{-1}\left(\frac{b}{a}\right) \). The angle may need to be adjusted based on the quadrant in which the complex number is located. In this case, \( w = \frac{5}{2} - 6i \), where \( a = \frac{5}{2} \) and \( b = -6 \). Calculate the direction angle using the arctangent function and adjust based on the quadrant if necessary.
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