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Direction Cosines | Calculus 3 Lesson 9 - JK Math
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How to Find Direction Cosines & Angles (Calculus 3 Lesson 9)
In this video you will learn how to represent the direction of a 3D vector by using the angles it makes with the positive x-axis, y-axis, and z-axis. These angles are found by using what are known as direction cosines. You will see where these directions cosines come from, how they work, and how you can use them to create a unit vector the represents the direction of a vector in 3D. Additionally, we look at an example problem of finding direction cosines and their respective angles.
This video series is designed to help students understand the concepts of Calculus 3 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!
Calculus 3 requires a solid understanding of concepts from calculus 2, calculus 1, precalculus, and algebra. This includes limits, differentiation, advanced integration techniques, applications of derivatives and integrals, polar coordinates, parametric equations, trigonometric functions, logarithms, factoring, equation manipulation, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!
Video Chapters:
0:00 Review of 2D Vectors & Unit Circle
1:57 What Are Direction Angles?
5:38 What are Direction Cosines?
15:52 Directions Cosines & Unit Vectors
20:20 Summary of Formulas
22:53 Example Part 1: Finding Direction Cosines
25:34 Example Part 2: Finding Direction Angles
28:13 Example Part 3: Show Sum of Squares = 1
⚡️Math Products I Recommend⚡️
⚡️Textbooks I Use⚡️
⚡️My Recording Equipment⚡️
(Commissions earned on qualifying purchases)
Find me on social media:
➡️ Instagram: @jk_mathematics
Found this video to be helpful? Consider giving this video a like and subscribing to the channel!
Thanks for watching! Any questions? Feedback? Leave a comment!
- Josh from JK Mathematics
#calculus
In this video you will learn how to represent the direction of a 3D vector by using the angles it makes with the positive x-axis, y-axis, and z-axis. These angles are found by using what are known as direction cosines. You will see where these directions cosines come from, how they work, and how you can use them to create a unit vector the represents the direction of a vector in 3D. Additionally, we look at an example problem of finding direction cosines and their respective angles.
This video series is designed to help students understand the concepts of Calculus 3 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture!
Calculus 3 requires a solid understanding of concepts from calculus 2, calculus 1, precalculus, and algebra. This includes limits, differentiation, advanced integration techniques, applications of derivatives and integrals, polar coordinates, parametric equations, trigonometric functions, logarithms, factoring, equation manipulation, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first!
Video Chapters:
0:00 Review of 2D Vectors & Unit Circle
1:57 What Are Direction Angles?
5:38 What are Direction Cosines?
15:52 Directions Cosines & Unit Vectors
20:20 Summary of Formulas
22:53 Example Part 1: Finding Direction Cosines
25:34 Example Part 2: Finding Direction Angles
28:13 Example Part 3: Show Sum of Squares = 1
⚡️Math Products I Recommend⚡️
⚡️Textbooks I Use⚡️
⚡️My Recording Equipment⚡️
(Commissions earned on qualifying purchases)
Find me on social media:
➡️ Instagram: @jk_mathematics
Found this video to be helpful? Consider giving this video a like and subscribing to the channel!
Thanks for watching! Any questions? Feedback? Leave a comment!
- Josh from JK Mathematics
#calculus
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