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To learn the pattern of the side lengths of a 45-45-90 triangle, students complete a gallery walk, a card sort activity starting with using the Pythagorean theorem, and activity to locate if there is an error in a presented problem and if so to identify what the error is.
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.
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.
6.01 Trigonometric Identities
In this video students will learn trigonometric identities, where they are derived from, and apply them in problems.
6.02 Solving Trigonometric Equations
In this video, students will learn to solve trigonometric equations for cases of a set interval and of all solutions.
6.03 Sum and Difference Formulas of Trigonometric Functions
In this video, students will apply the sum and difference formulas of trigonometry.
6.04 Double Angle and Half Angle Formulas of Trigonometric Functions
In this video, students will learn double and half angle formulas, and how they are derived, and will apply them to various problems.
6.05 Law of Sines and Cosines
In this video, students will expand their knowledge to oblique triangles and apply the laws of sines and cosines, followed by area equations for oblique triangles.
6.06 Trigonometric Word Problems
In this video, students will use their knowledge of trigonometry and apply that knowledge to word problems.
In this video, students are introduced to vectors, learn about vector addition and scalar multiplication, and then apply vectors to word problems.
7.01 Sequences and Series, Part 1
In this video, students will learn the definition of a sequence and how to calculate its general term.
7.02 Sequences and Series, Part 2
In this video, students will learn the definitions of a recursive sequence and a series.
7.03 Arithmetic Sequences and Series
In this video, students will learn the definition of an arithmetic sequence and how to calculate its general term.