For more information, please see full course syllabus of Calculus BC
For more information, please see full course syllabus of Calculus BC
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Vector Functions
- Displacement represented by magnitude and angel from +x-axis
- Vector has x (horizontal) and y (vertical) components
- Solving for vectors:
- Pythagorean theorem
Vector Functions
- Use the the Pythagorean Theorem to find r
- ||r|| = √{x2 + y2}
- = √{( − 1)2 + (6)2}
- = √{37}
- Use the arctangent function on x,y components to find θ
- θ = tan − 1([y/x])
- = tan − 1([6/( − 1)])
- = − 1.41 rad
- Use the the Pythagorean Theorem to find r
- ||r|| = √{x2 + y2}
- = √{( − 5)2 + ( − 12)2}
- = √{25 + 144}
- = √{169}
- = 13
- Use the arctangent function on x,y components to find θ
- θ = tan − 1([y/x])
- = tan − 1([( − 12)/( − 5)])
- = 1.18 rad
(Leave in terms of u)
- Use the the Pythagorean Theorem to find r
- ||r|| = √{x2 + y2}
- = √{(u)2 + (√{15} u)2}
- = √{u2 + 15u2}
- = √{16u2}
- = 4u
- Use the arctangent function on x,y components to find θ
- θ = tan − 1([(√{15} u)/u])
- = tan − 1(√{15} )
- = 1.317 rad
- Apply definitions for x and y
- x = rcosθ
- = 8cos([(7π)/4])
- = 4√2
- y = rsinθ
- = 8sin([(7π)/4])
- = − 4√2
- Apply definitions for x and y
- x = rcosθ
- = 32cos([(5π)/6])
- = − 16√3
- y = rsinθ
- = 32sin([(5π)/6])
- = 16
- Apply definitions for x and y
- x = rcosθ
- = 3cos([(13π)/8])
- = 1.15
- y = rsinθ
- = 3sin([(13π)/8])
- = − 2.77
- Substitute −4 for t
- Substitute − [(2√2 )/2] for t
v(t) = (2t,t4, − 30 + t)
- Answers will vary. In the case of v(t) = (2t,t4,30 − t)
- v(3) = (2(3),(3)4, − 30 + 3)
- = (6,81, − 27)

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.
Answer
Vector Functions
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.
- Intro 0:00
- Vector Functions 0:11
- 2 Parts
- Example 1 1:44
- Example 2 3:52
- Example 3 4:59
- Example 4 6:03
- Example 5 8:00
- Example 6 9:23
- Example 7 10:16
Mathematics: AP Calculus BC

John Zhu
Vector Functions
Slide Duration:Table of Contents
10m 10s
- Intro0:00
- Parametric Equations0:23
- Familiar Functions0:32
- Parametric Equation/ Function0:56
- Example 1: Graph Parametric Equation1:48
- Example 24:30
- Example 36:01
- Example 47:12
- Example 58:10
14m 54s
- Intro0:00
- Polar Coordinates0:09
- Definition0:11
- Example0:23
- Converting Polar Coordinates1:49
- Example: Convert Polar Equation to Cartesian Coordinates3:06
- Example: Convert Polar Equation to Cartesian Coordinates5:21
- Example: Find the Polar Representation6:51
- Example: Find the Polar Representation8:39
- Example: Sketch the Graph10:02
12m 5s
- Intro0:00
- Vector Functions0:11
- 2 Parts0:18
- Example 11:44
- Example 23:52
- Example 34:59
- Example 46:03
- Example 58:00
- Example 69:23
- Example 710:16
13m 15s
- Intro0:00
- Parametric Differentiation0:15
- Example 11:16
- Example 21:54
- Example 33:15
- Example 44:59
- Parametric Differentiation: Position, Speed & Acceleration7:45
- Example 58:32
- Example 610:37
10m 14s
- Intro0:00
- Polar Differentiation0:11
- Goal0:13
- Method0:24
- Example 10:52
- Example 24:27
- Example 37:03
6m 43s
- Intro0:00
- L'Hopitals Rule0:09
- Conditions0:14
- Limit0:36
- Example 11:21
- Example 22:38
- Example 34:09
- Example 45:01
19m 4s
- Intro0:00
- Integration by Parts0:12
- Formula0:31
- How It's Derived From Product Rule1:09
- Integration by Parts: Rules to Follow3:24
- Recap of the Rules4:13
- Example 14:29
- Example 27:04
- Example 38:40
- Example 413:48
- Example 515:36
22m 4s
- Intro0:00
- Integration by Partial Fractions: Goal0:08
- Example 12:10
- Example 27:10
- Example 310:06
- Example 414:23
- Example 516:26
19m 1s
- Intro0:00
- Improper Integrals0:06
- 3 Steps1:11
- Example 11:46
- Example 23:20
- Example 36:05
- Example 49:02
- Example 511:21
- Example 615:54
19m 16s
- Intro0:00
- Logistic Growth Function0:07
- Defining Variables0:40
- Equation Parts1:51
- Logistic Growth2:04
- Example 12:59
- Example 27:13
- Example 311:29
- Example 415:21
17m 40s
- Intro0:00
- Arc Length0:13
- Arc Length of a Normal Function0:24
- Example1:27
- Example 2: Arc Length for Parametric Curves3:31
- Example 3: Arc Length for Parametric Curves4:23
- Example 4: Arc Length for Parametric Curves8:05
- Example 5: Arc Length for Parametric Curves12:22
- Example 6: Arc Length for Polar Curves15:36
- Example 7: Arc Length for Polar Curves16:03
4m 33s
- Intro0:00
- Area for Parametric Curves: Parametric Function0:10
- Example 1: Area for Parametric Curves0:35
- Area for Parametric Curves: Polar Function2:50
- Example 2: Area for Polar Curves3:18
7m 10s
- Intro0:00
- Sequences: Definition0:09
- Definition0:31
- Example 11:07
- Sequences: Convergence2:02
- Example 12:52
- Example 23:36
- Example 34:47
- Example 46:16
10m 59s
- Intro0:00
- Geometric Series0:07
- Definition0:24
- Expanded Form0:39
- Convergence Rules1:00
- Example 1: Convergence1:22
- Example 2: Convergence2:36
- Example 3: Convergence3:45
- Sum of Series5:04
- Sum of First n Terms5:14
- Sum of Series5:24
- Example 1: Sum of Series5:39
- Example 2: Sum of Series7:15
- Example 3: Sum of Series8:24
- Example 4: Sum of Series9:36
3m 58s
- Intro0:00
- Harmonic Series0:08
- P-Series1:17
- Example 1: P-Series Test2:22
- Example 2: P-Series Test3:06
11m 31s
- Intro0:00
- Integral Test0:09
- Example 10:54
- Example 24:00
- Example 37:59
- Example 49:47
7m 47s
- Intro0:00
- Comparison Test0:10
- Example 11:07
- Example 22:33
- Example 34:20
- Example 46:29
9m 40s
- Intro0:00
- Limit Comparison Test0:09
- Conditions0:31
- Example 11:01
- Example 22:53
- Example 34:15
- Example 46:19
11m 20s
- Intro0:00
- Ratio Test0:09
- Example 10:57
- Example 22:55
- Example 36:27
- Example 48:36
9m 11s
- Intro0:00
- Alternating Series0:08
- Convergence Test0:59
- Example 11:27
- Example 22:42
- Example 34:57
- Example 46:37
7m 13s
- Intro0:00
- Absolute Convergence0:12
- Example 10:52
- Example 23:42
- Example 35:21
12m 52s
- Intro0:00
- Power Series0:09
- Definition0:19
- Radius & Interval of Convergence2:07
- Example 12:28
- Example 24:18
- Example 36:20
- Example 49:11
15m 11s
- Intro0:00
- Taylor Series0:06
- MacLaurin Series0:45
- Example 11:02
- Example 22:45
- Example 36:04
- Example 48:23
- Example 511:49
16m 40s
- Intro0:00
- Operations0:07
- Example 1: Substitution1:05
- Example 2: Substitution3:41
- Example 3: Differentiation/ Integration5:39
- Example 4: Differentiation/ Integration9:55
- Example 5: Multiplying/ Dividing12:32
- Example 6: Multiplying/ Dividing14:50
7m 9s
- Intro0:00
- Power Series: Lagrange Error0:06
- Lagrange Remainder0:21
- Lagrange Error Bound0:50
- Example 11:06
- Example 23:27
15m 45s
- Intro0:00
- Practice Problem 10:10
- Practice Problem 21:19
- Practice Problem 32:33
- Practice Problem 45:25
- Practice Problem 56:32
- Practice Problem 69:11
- Practice Problem 711:31
- Practice Problem 813:08
- Practice Problem 914:16
21m 38s
- Intro0:00
- Practice Problem 100:12
- Practice Problem 113:03
- Practice Problem 124:53
- Practice Problem 136:56
- Practice Problem 149:10
- Practice Problem 1512:17
- Practice Problem 1614:43
- Practice Problem 1716:18
- Practice Problem 1818:34
17m 31s
- Intro0:00
- Practice Problem 190:09
- Practice Problem 203:03
- Practice Problem 214:07
- Practice Problem 225:41
- Practice Problem 238:48
- Practice Problem 2411:16
- Practice Problem 2512:53
- Practice Problem 2614:12
- Practice Problem 2715:21
14m 17s
- Intro0:00
- Practice Problem 280:08
- Practice Problem 291:19
- Practice Problem 302:15
- Practice Problem 314:19
- Practice Problem 326:54
- Practice Problem 338:13
- Practice Problem 349:03
- Practice Problem 3510:21
- Practice Problem 3611:42
22m 45s
- Intro0:00
- Practice Problem 370:10
- Practice Problem 384:09
- Practice Problem 397:21
- Practice Problem 409:42
- Practice Problem 4111:35
- Practice Problem 4214:01
- Practice Problem 4315:50
- Practice Problem 4416:43
- Practice Problem 4519:35
9m 55s
- Intro0:00
- Practice Problem 1a0:08
- Practice Problem 1b1:30
- Practice Problem 1c3:08
- Practice Problem 2a3:50
- Practice Problem 2b5:40
- Practice Problem 2c7:24
10m 8s
- Intro0:00
- Practice Problem 3a0:09
- Practice Problem 3b3:01
- Practice Problem 4a3:55
- Practice Problem 4b5:43
13m 58s
- Intro0:00
- Practice Problem 5a0:07
- Practice Problem 5b2:21
- Practice Problem 5c4:21
- Practice Problem 6a6:16
- Practice Problem 6b8:57
- Practice Problem 6c11:03
0 answers
Post by annac97 on April 23, 2015
For the first example, can you just use a -2 to plug into the equation? So you'd do inverse tan(-2/5) instead?