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6.08 Bonus Video: Law of Sines—The Ambiguous Case
The Law of Sines can be used to solve for sides and angles of oblique triangles. However, in some cases more than one triangle may satisfy the given conditions. We refer to this as an ambiguous case.
Study Edge Precalculus
Precalculus is the preparation for calculus. The course approaches is designed to strengthen and enhance conceptual understanding and mathematical reasoning used when modeling and solving mathematical and real-world problems. Students systematically work with functions and their multiple representations. Precalculus can deepen students' mathematical understanding and fluency with algebra and trigonometry and extends their ability to make connections and apply concepts and procedures at higher levels. Students will investigate and explore mathematical ideas, develop multiple strategies for analyzing complex situations, and use technology to build understanding, make connections between representations, and provide support in solving problems (TAC §111.42(b)(3)).
This video book is brought to you by TEA and Study Edge. It may be used to teach an entire Precalculus course or to supplement traditional Precalculus textbooks.
This open-education-resource instructional material by TEA is licensed under a Creative Commons Attribution 4.0 International Public License in accordance with Chapter 31 of the Texas Education Code.
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5.01 Radians and Degree Measurements
In this video, students will learn the basics of angle measurements, definitions of various types of angles, radians and degrees, along with arc length and area of a sector.
5.02 Linear and Angular Velocity
In this video, students will learn about angular and linear velocity and how each relates to unit conversions.
5.03 Trigonometric Ratios
In this video, we will define the trigonometric ratios in terms of the sides of a right triangle.
5.04 Trigonometric Angles and the Unit Circle
In this video, students will learn special angles and the unit circle, and learn how to apply them.
5.05 Graphs of Sine and Cosine
In this video, students will learn how to graph sine and cosine and how to interpret graphs of sine and cosine.
5.06 Graphs of Secant and Cosecant
In this video, students will learn how to graph and interpret graphs of secant and cosecant, and how secant and cosecant relate to sine and cosine.
5.07 Graphs of Tangent and Cotangent
In this video, students will learn how to graph and how to interpret graphs of tangent and cotangent.
5.08 Inverse Trigonometric Functions and Graphs
In this video, students will explore the relationship between trigonometric functions and their inverses.
Given examples, students will recognize the importance of taxonomy to the scientific community.
Taxonomy: Major Groups
Given illustrations or descriptions, students will determine the classification of organisms into domains and kingdoms.
Given illustrations or scenarios, the student will identify an enzyme and the outcome of its action.
Animal System Interactions
Given illustrations, descriptions, or scenarios, students will describe the interactions that occur among systems in humans.
Mechanisms of Genetics: Protein Synthesis
Given illustrations or partial DNA or mRNA sequences, students will identify the processes and purposes of transcription and translation.
Given scenarios, illustrations, or descriptions, the student will describe the flow of matter through carbon and nitrogen cycles and describe the consequences of disrupting these cycles.
Homeostasis: Ecological Systems
Given images, videos, or scenarios, identify and describe the responses of organisms, populations, and communities to various changes in their external environment.
Biological Systems: System Organization
Given illustrations or descriptions, students will relate the levels of organization to each other and to the whole system.
Biological Systems: Homeostasis
Identify and describe internal feedback mechanisms involved in maintaining homeostasis given scenarios, illustrations, or descriptions.
Relationships Between Organisms: Food Chains, Webs, and Pyramids
Given illustrations, students will analyze the flow of matter and energy in food chains, food webs, and ecological pyramids.