Trigonometry (Algebra 2 Curriculum - Unit 12) | All Things Algebra®
- Google Apps™
What educators are saying
Also included in.
Description
Due to the length of this Trigonometry Unit Bundle , it is divided into two parts with two unit tests. In addition to the unit tests, each part includes guided notes, homework assignments, quizzes, and study guides to cover the following topics:
Unit 12 Part I:
• Pythagorean Theorem
• Special Right Triangles
• Trigonometric Functions (sin, cos, tan, csc, sec, cot)
• Finding Side and Angle Measures
• Applications: Angle of Elevation and Depression
• Angles in Standard Position
• Converting between Degrees and Radians
• Coterminal and Reference Angles
• Trigonometric Functions in the Coordinate Plane
• The Unit Circle
• Law of Sines
• Law of Cosines
• Area of Triangles
• Applications of Law of Sines, Law of Cosines, and Area
Unit 12 Part II:
• Graphing Trigonometric Functions
• Trigonometric Identities
• Sum and Difference of Angle Identities
• Double-Angle and Half-Angle Identities
• Solving Trigonometric Equations
ADDITIONAL COMPONENTS INCLUDED:
(1) Links to Instructional Videos: Links to videos of each lesson in the unit are included. Videos were created by fellow teachers for their students using the guided notes and shared in March 2020 when schools closed with no notice. Please watch through first before sharing with your students. Many teachers still use these in emergency substitute situations. (2) Editable Assessments: Editable versions of each quiz and the unit test are included. PowerPoint is required to edit these files. Individual problems can be changed to create multiple versions of the assessment. The layout of the assessment itself is not editable. If your Equation Editor is incompatible with mine (I use MathType), simply delete my equation and insert your own.
(3) Google Slides Version of the PDF: The second page of the Video links document contains a link to a Google Slides version of the PDF. Each page is set to the background in Google Slides. There are no text boxes; this is the PDF in Google Slides. I am unable to do text boxes at this time but hope this saves you a step if you wish to use it in Slides instead!
This resource is included in the following bundle(s):
Algebra 2 Curriculum
More Algebra 2 Units:
Unit 1 – Equations and Inequalities
Unit 2 – Linear Functions and Systems
Unit 3 – Parent Functions and Transformations
Unit 4 – Solving Quadratics and Complex Numbers
Unit 5 – Polynomial Functions
Unit 6 – Radical Functions
Unit 7 – Exponential and Logarithmic Functions
Unit 8 – Rational Functions
Unit 9 – Conic Sections
Unit 10 – Sequences and Series
Unit 11 – Probability and Statistics
LICENSING TERMS: This purchase includes a license for one teacher only for personal use in their classroom. Licenses are non-transferable , meaning they can not be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses. If you are a coach, principal, or district interested in transferable licenses to accommodate yearly staff changes, please contact me for a quote at [email protected].
COPYRIGHT TERMS: This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.
© All Things Algebra (Gina Wilson), 2012-present
Questions & Answers
All things algebra.
- We're hiring
- Help & FAQ
- Privacy policy
- Student privacy
- Terms of service
- Tell us what you think
3 π 2 3 π 2
−135 ° −135 °
7 π 10 7 π 10
α = 150° α = 150°
β = 60° β = 60°
7 π 6 7 π 6
215 π 18 = 37.525 units 215 π 18 = 37.525 units
− 3 π 2 − 3 π 2 rad/s
1655 kilometers per hour
7.2 Right Triangle Trigonometry
sin t = 33 65 , cos t = 56 65 , tan t = 33 56 , sec t = 65 56 , csc t = 65 33 , cot t = 56 33 sin t = 33 65 , cos t = 56 65 , tan t = 33 56 , sec t = 65 56 , csc t = 65 33 , cot t = 56 33
sin ( π 4 ) = 2 2 , cos ( π 4 ) = 2 2 , tan ( π 4 ) = 1 , sec ( π 4 ) = 2 , csc ( π 4 ) = 2 , cot ( π 4 ) = 1 sin ( π 4 ) = 2 2 , cos ( π 4 ) = 2 2 , tan ( π 4 ) = 1 , sec ( π 4 ) = 2 , csc ( π 4 ) = 2 , cot ( π 4 ) = 1
adjacent = 10 ; opposite = 10 3 ; adjacent = 10 ; opposite = 10 3 ; missing angle is π 6 π 6
About 52 ft
7.3 Unit Circle
cos ( t ) = − 2 2 , sin ( t ) = 2 2 cos ( t ) = − 2 2 , sin ( t ) = 2 2
cos ( π ) = − 1 , sin ( π ) = 0 cos ( π ) = − 1 , sin ( π ) = 0
sin ( t ) = − 7 25 sin ( t ) = − 7 25
approximately 0.866025403
- ⓐ cos ( 315° ) = 2 2 , sin ( 315° ) = – 2 2 cos ( 315° ) = 2 2 , sin ( 315° ) = – 2 2
- ⓑ cos ( − π 6 ) = 3 2 , sin ( − π 6 ) = − 1 2 cos ( − π 6 ) = 3 2 , sin ( − π 6 ) = − 1 2
( 1 2 , − 3 2 ) ( 1 2 , − 3 2 )
7.4 The Other Trigonometric Functions
sin t = − 2 2 cos t = 2 2 , tan t = − 1 , s e c t = 2 , csc t = − 2 , cot t = − 1 sin t = − 2 2 cos t = 2 2 , tan t = − 1 , s e c t = 2 , csc t = − 2 , cot t = − 1
sin π 3 = 3 2 , cos π 3 = 1 2 , tan π 3 = 3 , s e c π 3 = 2 , c s c π 3 = 2 3 3 , c o t π 3 = 3 3 sin π 3 = 3 2 , cos π 3 = 1 2 , tan π 3 = 3 , s e c π 3 = 2 , c s c π 3 = 2 3 3 , c o t π 3 = 3 3
sin ( − 7 π 4 ) = 2 2 , cos ( − 7 π 4 ) = 2 2 , tan ( − 7 π 4 ) = 1 , sec ( − 7 π 4 ) = 2 , csc ( − 7 π 4 ) = 2 , cot ( − 7 π 4 ) = 1 sin ( − 7 π 4 ) = 2 2 , cos ( − 7 π 4 ) = 2 2 , tan ( − 7 π 4 ) = 1 , sec ( − 7 π 4 ) = 2 , csc ( − 7 π 4 ) = 2 , cot ( − 7 π 4 ) = 1
sin t sin t
cos t = − 8 17 , sin t = 15 17 , tan t = − 15 8 csc t = 17 15 , cot t = − 8 15 cos t = − 8 17 , sin t = 15 17 , tan t = − 15 8 csc t = 17 15 , cot t = − 8 15
sin t = − 1 , cos t = 0 , tan t = Undefined sec t = Undefined, csc t = − 1 , cot t = 0 sin t = − 1 , cos t = 0 , tan t = Undefined sec t = Undefined, csc t = − 1 , cot t = 0
sec t = 2 , csc t = 2 , tan t = 1 , cot t = 1 sec t = 2 , csc t = 2 , tan t = 1 , cot t = 1
≈ − 2.414 ≈ − 2.414
7.1 Section Exercises
Whether the angle is positive or negative determines the direction. A positive angle is drawn in the counterclockwise direction, and a negative angle is drawn in the clockwise direction.
Linear speed is a measurement found by calculating distance of an arc compared to time. Angular speed is a measurement found by calculating the angle of an arc compared to time.
4 π 3 4 π 3
2 π 3 2 π 3
7 π 2 ≈ 11.00 in 2 7 π 2 ≈ 11.00 in 2
81 π 20 ≈ 12.72 cm 2 81 π 20 ≈ 12.72 cm 2
π 2 π 2 radians
−3 π −3 π radians
π π radians
5 π 6 5 π 6 radians
5.02 π 3 ≈ 5.26 5.02 π 3 ≈ 5.26 miles
25 π 9 ≈ 8.73 25 π 9 ≈ 8.73 centimeters
21 π 10 ≈ 6.60 21 π 10 ≈ 6.60 meters
104.7198 cm 2
0.7697 in 2
8 π 9 8 π 9
1320 1320 rad/min 210.085 210.085 RPM
7 7 in./s, 4.77 RPM , 28.65 28.65 deg/s
1 , 809 , 557.37 mm/min = 1 , 809 , 557.37 mm/min = 30.16 m/s 30.16 m/s
5.76 5.76 miles
794 miles per hour
2,234 miles per hour
11.5 inches
7.2 Section Exercises
The tangent of an angle is the ratio of the opposite side to the adjacent side.
For example, the sine of an angle is equal to the cosine of its complement; the cosine of an angle is equal to the sine of its complement.
b = 20 3 3 , c = 40 3 3 b = 20 3 3 , c = 40 3 3
a = 10,000 , c = 10,00.5 a = 10,000 , c = 10,00.5
b = 5 3 3 , c = 10 3 3 b = 5 3 3 , c = 10 3 3
5 29 29 5 29 29
5 41 41 5 41 41
c = 14 , b = 7 3 c = 14 , b = 7 3
a = 15 , b = 15 a = 15 , b = 15
b = 9.9970 , c = 12.2041 b = 9.9970 , c = 12.2041
a = 2.0838 , b = 11.8177 a = 2.0838 , b = 11.8177
a = 55.9808 , c = 57.9555 a = 55.9808 , c = 57.9555
a = 46.6790 , b = 17.9184 a = 46.6790 , b = 17.9184
a = 16.4662 , c = 16.8341 a = 16.4662 , c = 16.8341
498.3471 ft
22.6506 ft
368.7633 ft
7.3 Section Exercises
The unit circle is a circle of radius 1 centered at the origin.
Coterminal angles are angles that share the same terminal side. A reference angle is the size of the smallest acute angle, t , t , formed by the terminal side of the angle t t and the horizontal axis.
The sine values are equal.
60° , 60° , Quadrant IV, sin ( 300° ) = − 3 2 sin ( 300° ) = − 3 2 , cos ( 300° ) = 1 2 cos ( 300° ) = 1 2
45° , 45° , Quadrant II, sin ( 135° ) = 2 2 sin ( 135° ) = 2 2 , cos ( 135° ) = − 2 2 cos ( 135° ) = − 2 2
60° , 60° , Quadrant II, sin ( 120° ) = 3 2 sin ( 120° ) = 3 2 , cos ( 120° ) = − 1 2 cos ( 120° ) = − 1 2
30° , 30° , Quadrant II, sin ( 150° ) = 1 2 sin ( 150° ) = 1 2 , cos ( 150° ) = − 3 2 cos ( 150° ) = − 3 2
π 6 , π 6 , Quadrant III, sin ( 7 π 6 ) = − 1 2 sin ( 7 π 6 ) = − 1 2 , cos ( 7 π 6 ) = − 3 2 cos ( 7 π 6 ) = − 3 2
π 4 , π 4 , Quadrant II, sin ( 3 π 4 ) = 2 2 sin ( 3 π 4 ) = 2 2 , cos ( 4 π 3 ) = − 2 2 cos ( 4 π 3 ) = − 2 2
π 3 , π 3 , Quadrant II, sin ( 2 π 3 ) = 3 2 sin ( 2 π 3 ) = 3 2 , cos ( 2 π 3 ) = − 1 2 cos ( 2 π 3 ) = − 1 2
π 4 , π 4 , Quadrant IV, sin ( 7 π 4 ) = − 2 2 , cos ( 7 π 4 ) = 2 2 sin ( 7 π 4 ) = − 2 2 , cos ( 7 π 4 ) = 2 2
− 15 4 − 15 4
( −10 , 10 3 ) ( −10 , 10 3 )
( –2.778 , 15.757 ) ( –2.778 , 15.757 )
[ –1 , 1 ] [ –1 , 1 ]
sin t = 1 2 , cos t = − 3 2 sin t = 1 2 , cos t = − 3 2
sin t = − 2 2 , cos t = − 2 2 sin t = − 2 2 , cos t = − 2 2
sin t = 3 2 , cos t = − 1 2 sin t = 3 2 , cos t = − 1 2
sin t = − 2 2 , cos t = 2 2 sin t = − 2 2 , cos t = 2 2
sin t = 0 , cos t = − 1 sin t = 0 , cos t = − 1
sin t = − 0.596 , cos t = 0.803 sin t = − 0.596 , cos t = 0.803
sin t = 1 2 , cos t = 3 2 sin t = 1 2 , cos t = 3 2
sin t = − 1 2 , cos t = 3 2 sin t = − 1 2 , cos t = 3 2
sin t = 0.761 , cos t = − 0.649 sin t = 0.761 , cos t = − 0.649
sin t = 1 , cos t = 0 sin t = 1 , cos t = 0
− 6 4 − 6 4
( 0 , –1 ) ( 0 , –1 )
37.5 seconds, 97.5 seconds, 157.5 seconds, 217.5 seconds, 277.5 seconds, 337.5 seconds
7.4 Section Exercises
Yes, when the reference angle is π 4 π 4 and the terminal side of the angle is in quadrants I and III. Thus, a x = π 4 , 5 π 4 , x = π 4 , 5 π 4 , the sine and cosine values are equal.
Substitute the sine of the angle in for y y in the Pythagorean Theorem x 2 + y 2 = 1. x 2 + y 2 = 1. Solve for x x and take the negative solution.
The outputs of tangent and cotangent will repeat every π π units.
2 3 3 2 3 3
− 2 3 3 − 2 3 3
− 3 3 − 3 3
sin t = − 2 2 3 sin t = − 2 2 3 , sec t = − 3 sec t = − 3 , csc t = − 3 2 4 csc t = − 3 2 4 , tan t = 2 2 tan t = 2 2 , cot t = 2 4 cot t = 2 4
sec t = 2 , sec t = 2 , csc t = 2 3 3 , csc t = 2 3 3 , tan t = 3 , tan t = 3 , cot t = 3 3 cot t = 3 3
− 2 2 − 2 2
sin t = 2 2 sin t = 2 2 , cos t = 2 2 cos t = 2 2 , tan t = 1 tan t = 1 , cot t = 1 cot t = 1 , sec t = 2 sec t = 2 , csc t = 2 csc t = 2
sin t = − 3 2 sin t = − 3 2 , cos t = − 1 2 cos t = − 1 2 tan t = 3 tan t = 3 , cot t = 3 3 cot t = 3 3 , sec t = − 2 sec t = − 2 , csc t = − 2 3 3 csc t = − 2 3 3
sin ( t ) ≈ 0.79 sin ( t ) ≈ 0.79
csc t ≈ 1.16 csc t ≈ 1.16
sin t cos t = tan t sin t cos t = tan t
13.77 hours, period: 1000 π 1000 π
3.46 inches
Review Exercises
− 7 π 6 − 7 π 6
10.385 meters
2 π 11 2 π 11
1036.73 miles per hour
a = 10 3 , c = 2 106 3 a = 10 3 , c = 2 106 3
a = 5 3 2 , b = 5 2 a = 5 3 2 , b = 5 2
369.2136 ft
all real numbers
cosine, secant
Practice Test
6.283 centimeters
3.351 feet per second, 2 π 75 2 π 75 radians per second
a = 9 2 , b = 9 3 2 a = 9 2 , b = 9 3 2
real numbers
This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.
Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.
Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites
- Authors: Jay Abramson
- Publisher/website: OpenStax
- Book title: Algebra and Trigonometry
- Publication date: Feb 13, 2015
- Location: Houston, Texas
- Book URL: https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction-to-prerequisites
- Section URL: https://openstax.org/books/algebra-and-trigonometry/pages/chapter-7
© Dec 8, 2021 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.
IMAGES
VIDEO
COMMENTS
Other Math questions and answers. Name: Date: Unit 12: Trigonometry Bell: — Homework 3: Angles and Angle Measure ** This is a 2-page document ** Directions: Convert each measure to radians. 1. 225 2. 20 3.-255 4.-140" 5. 75 6.-300 Directions: Convert each measure to degrees. 7.7 831- 12. Directions: Sketch each angle.
Exercise 100. At Quizlet, we're giving you the tools you need to take on any subject without having to carry around solutions manuals or printing out PDFs! Now, with expert-verified solutions from Trigonometry 12th Edition, you'll learn how to solve your toughest homework problems. Our resource for Trigonometry includes answers to chapter ...
Name: Date: Unit 8: Right Triangles & Trigonometry Homework 5: Trigonometry: Finding Sides and Angles ** This is a 2-page document! ** -tan 39 X: 33,3 Directions: Solve for x. Round to the nearest tenth. Cos 143 = 52 = Cos 16: fin X = 5 X: COS-I (£9 @ Gina Wilson (All Things Algebraø, LLC), 2014-2018. Name: Date: Unit 8: Right Triangles ...
12.3_notes_evaluating_trig.pdf. File Size: 322 kb. File Type: pdf. Download File. Homework Solutions. Homework Solutions will now be posted after the homework has been stamped or collected. Please try the problems on your own and ask questions in class!
Unit 12: trigonometry, homework 3: angles and angle measure Get the answers you need, now! Skip to main content ... Answer: Trigonometry: 19) hypotenuse² = base² + altitude² ... Unit 8 homework 5 trigonometry finding sides and angles answer key. heart. 1. verified. Verified answer.
Verified answer. Unit 8 homework 5 trigonometry finding sides and angles answer key. heart. 1. verified. Verified answer. Jonathan and his sister Jennifer have a combined age of 48. If Jonathan is twice as old as his sister, how old is Jennifer. star.
This is a 5 part worksheet: Part I Model Problems. Part II Practice Problems (1-6) Part III Practice (harder) & Word Problems (7 - 18) Part IV Challenge Problems. Part V Answer Key.
1 triangle. Ambiguous Cases: If a>b. 1 right triangle. Ambiguous Cases: If a=x. 0 triangles. Ambiguous Cases: If a<x. 2 triangles. Ambiguous Cases: If a>x. Study with Quizlet and memorize flashcards containing terms like trigonometric ratios, oblique, law of cosines and more.
Exercise 96. At Quizlet, we're giving you the tools you need to take on any subject without having to carry around solutions manuals or printing out PDFs! Now, with expert-verified solutions from Trigonometry 6th Edition, you'll learn how to solve your toughest homework problems. Our resource for Trigonometry includes answers to chapter ...
To start solving problem 1, use the Pythagorean Theorem with the given legs of the right triangle: x 2 = 14 2 + 10 2. Name: Unit 12: Trigonometry Date: Bell: Homework 1: Pythagorean Theorem, Special Right Triangles, & Trig Functions ** This is a 2-page document ** Directions: Find each missing length. Give all answers in simplest radical form. 1.
1. The terms of a polynomial do not have to have a common factor for the entire polynomial to be factorable. For example, 4x2 and −9y2 don't have a common factor, but the whole polynomial is still factorable: 4x2−9y2 = (2x + 3y)(2x−3y). 3. Divide the x term into the sum of two terms, factor each portion of the expression separately, and ...
1. The cofunction identities apply to complementary angles. Viewing the two acute angles of a right triangle, if one of those angles measures x, the second angle measures π 2 − x. Then sinx = cos(π 2 − x). The same holds for the other cofunction identities. The key is that the angles are complementary.
Find step-by-step solutions and answers to Trigonometry - 9780134217437, as well as thousands of textbooks so you can move forward with confidence. ... Exercise 12. Exercise 13. Exercise 14. Exercise 15. Exercise 16. Exercise 17. Exercise 18. Exercise 19. Exercise 20. ... Section 3-3: The Unit Circle and Circular Functions. Section 3-4: Linear ...
Exercise 113. Exercise 114. Exercise 115. Exercise 116. At Quizlet, we're giving you the tools you need to take on any subject without having to carry around solutions manuals or printing out PDFs! Now, with expert-verified solutions from Trigonometry 10th Edition, you'll learn how to solve your toughest homework problems.
In addition to the unit tests, each part includes guided notes, homework assignments, quizzes, and study guides to cover the following topics: Unit 12 Part I: • Pythagorean Theorem. • Special Right Triangles. • Trigonometric Functions (sin, cos, tan, csc, sec, cot) • Finding Side and Angle Measures. • Applications: Angle of Elevation ...
Algebra questions and answers; Name: Date: Unit 12: Trigonometry Bell: Homework 2: Finding Side and Angle Mease ** This is a 2-page document! ** Directions: Find each missing measure. Round all answers to the nearest tenth. 1. 15 26 24 49 3. 4. 5 67 18 5. 30 53 7. 32 13 35 15 8. 10 27 26.2 19
Advanced Math. Advanced Math questions and answers. Name: Unit 12 Test Study Guide (Trigonometry - Part 1) Date: Block Topic Trigonometrie Functions 1. Find the values of the six trigonometric functions for angle 1). Give answers in simplest form. cos o . _ 2. If tan find the remaining trigonometric functions. 3.
Chapter 8: At Quizlet, we're giving you the tools you need to take on any subject without having to carry around solutions manuals or printing out PDFs! Now, with expert-verified solutions from Trigonometry 8th Edition, you'll learn how to solve your toughest homework problems. Our resource for Trigonometry includes answers to chapter ...
7.3 Section Exercises. 1. The unit circle is a circle of radius 1 centered at the origin. 3. Coterminal angles are angles that share the same terminal side. A reference angle is the size of the smallest acute angle, t, formed by the terminal side of the angle t and the horizontal axis. 5.
Find step-by-step solutions and answers to Trigonometry - 9780357455210, as well as thousands of textbooks so you can move forward with confidence. ... The Unit Circle. Section 1.3: Right Triangle Trigonometry. Section 1.4: Trigonometric Functions of Any Angle. Section 1.5: ... Exercise 12. Exercise 13. Exercise 14. Exercise 15. Exercise 16 ...
Precalculus questions and answers; Name: Date: Unit 12: Trigonometry Bell: Homework 11: Fundamental Trig Identities ** This is a 2-page document! ** Directions: Find the exact value of each expression if 90° <0<180°. 1 4 1. If cos = find cote. 2. If csc = find sece. -- Directions: Find the exact value of each expression if 270° <0 < 360°. 3.
Algebra questions and answers; Name: Unit 12: Trigonometry Homework 4: The Unit Circle Date: Bell: 1. Which trig functions are positive for angles terminating in Quadrant IV? 2. Which trig functions are negative for angles terminating in Quadrant 11? 3. If cos 0 < 0, which quadrant(s) could the terminal side of olie? 4.