Curriculum Information Essential Knowledge and Skills Key Vocabulary Essential Questions and Understandings Teacher and Elaborations Topic Triangular and Circular Trigonometric Functions Virginia Standard T.3 The student will find, without the aid of a calculator, the values of the trigonometric functions of the special angles and their related angles as found in the unit circle. This will include converting angle measures from radians to degrees and vice versa. The student will use problem solving, mathematical communication, mathematical reasoning, connections and representations to: Find trigonometric function values of specials angles and their related angles in both degrees and radians. Apply the properties of the unit circle without using a calculator. Use a conversion factor to convert from radians to degrees and vice versa without using a calculator. Key Vocabulary coterminal angles degrees quadrantal angles radian revolution unit circle Essential Questions What is the relationship between radians and degrees? What is the relationship between families of coterminal angles? What is meant by the special angles? Essential Understandings Special angles are widely used in mathematics. Unit circle properties will allow special-angle and related-angle trigonometric values to be found without the aid of a calculator. Degrees and radians are units of angle measure. A radian is the measure of the central angle that is determined by an arc whose length is the same as the radius of the circle. Teacher and Elaborations The two most common used to measure angles are radians and degrees. The radian measure of an angle in standard position is defined as the length of the corresponding arc divided by the radius of the circle (). One degree, 1°, is the result from a rotation of of a complete revolution about the vertex in the positive direction. A full revolution (counterclockwise) corresponds to 360º. To convert radians to degrees and vice versa, multiply by the appropriate conversion factor . Multiples, between 0 and 2π, of first quadrant special angles are found without the aid of a calculator. Angles that measure greater than 2π can be formed by adding or subtracting a multiple of 2π to its coterminal angle measuring between 0 and 2π. Two angles in standard position with the same initial and terminal sides are called coterminal angles. (continued)
Curriculum Information Resources Sample Instructional Strategies and Activities Topic Triangular and Circular Trigonometric Functions Virginia Standard T.3 Text: Trigonometry, Sixth Edition, 2006, McDougal Littell/Houghten Mifflin PWC Mathematics website Virginia Department of Education website
Curriculum Information Resources Sample Instructional Strategies and Activities Trigonometric Equations, Graphs, and Practical Problems Virginia Standard T.6 Text: Trigonometry, Sixth Edition, 2006, McDougal Littell/Houghten Mifflin PWC Mathematics website Virginia Department of Education website
Curriculum Information Resources Sample Instructional Strategies and Activities Topic Inverse Trigonometric Functions Virginia Standard T.7 Text: Trigonometry, Sixth Edition, 2006, McDougal Littell/Houghten Mifflin PWC Mathematics website Virginia Department of Education website
Curriculum Information Essential Questions and Understandings Teacher Notes and Elaborations Topic Trigonometric Equations, Graphs, and Practical Problems Virginia Standard T.9 The student will identify, create, and solve real-world problems involving triangles. Techniques will include using the trigonometric functions, the Pythagorean Theorem, the Law of Sines, and the Law of Cosines. Teacher Notes and Elaborations (continued) Many quantities in mathematics involve magnitudes. These quantities are called scalar. Other quantities called vector quantities, involve both magnitude and direction. A vector quantity is often represented with a directed line segment, which is called a vector. The length of the vector represents the magnitude of the vector quantity. Each vector has a horizontal and vertical component. Vectors may be added and subtracted. Sum and Difference Formulas:
Curriculum Information Resources Sample Instructional Strategies and Activities Topic Trigonometric Equations, Graphs, and Practical Problems Virginia Standard T.9 Text: Trigonometry, Sixth Edition, 2006, McDougal Littell/Houghten Mifflin PWC Mathematics website Virginia Department of Education website