Curriculum Information Essential Knowledge and Skills Essential Questions and Understandings Key Vocabulary Teacher and Elaborations Topic The student will use problem solving, Essential Questions Triangular and Circular Trigonometric mathematical communication, What is the relationship between radians and degrees? Functions mathematical reasoning, connections What is the relationship between families of coterminal angles? and representations to: What is meant by the special angles? Find trigonometric function values of specials angles and their related angles Virginia Standard T.3 Essential Understandings The student will find, without the aid of in both degrees and radians. Special angles are widely used in mathematics. a calculator, the values of the Apply the properties of the unit circle Unit circle properties will allow special-angle and related-angle trigonometric values to trigonometric functions of the special without using a calculator. be found without the aid of a calculator. angles and their related angles as found Use a conversion factor to convert from Degrees and radians are units of angle measure. in the unit circle. This will include radians to degrees and vice versa A radian is the measure of the central angle that is determined by an arc whose length is converting angle measures from radians without using a calculator. the same as the radius of the circle. to degrees and vice versa. Teacher and Elaborations Key Vocabulary The two most common used to measure angles are radians and degrees. The radian coterminal angles measure of an angle in standard position is defined as the length of the corresponding arc degrees divided by the radius of the circle (). One degree, 1°, is the result from a rotation of of a quadrantal angles complete about the vertex in the positive direction. A full revolution revolution radian (counterclockwise) corresponds to 360º. revolution unit circle 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 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)
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