F.TF.2 Explain how the unit Ability to connect Apply values of sine and cosine for special angles to develop circle in the coordinate plane knowledge of special coordinates of points on the unit circle in the first quadrant. enables the extension of right triangles gained in (Cosine is the x coordinate and sine is the y coordinate.) trigonometric functions to all Geometry to evaluating Use sine and cosine of reference angles to develop real numbers, interpreted as trigonometric functions coordinates for other quadrants radian measures of angles at any domain value Recognize that co-terminal angles have the same traversed counterclockwise Ability to extend to trigonometric function values. around the unit circle. angles beyond [-], using (additional) counterclockwise as the positive direction of rotation F.TF.5 Choose trigonometric Ability to recognize Relate transformations of other functions to trigonometric functions to model periodic graphs of parent functions to highlight amplitude (vertical stretch or phenomena with specified functions of compression), period (horizontal stretch or compression) amplitude, frequency, and trigonometric functions and phase shift (horizontal translation), and midline (vertical midline. ★ shift.) Ability to connect (additional) contextual situations to Recognize that period and frequency are reciprocals. appropriate Recognize that the graphs of sine and cosine functions have trigonometric function: an amplitude, while the graphs of other trigonometric e.g. using sine or cosine functions do not because there is no maximum or minimum to model cyclical value. behavior
F.TF.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. (additional) Ability to connect knowledge of special right triangles gained in Geometry to evaluating trigonometric functions at any domain value Ability to extend to angles beyond [-], using counterclockwise as the positive direction of rotation Apply values of sine and cosine for special angles to develop coordinates of points on the unit circle in the first quadrant. (Cosine is the x coordinate and sine is the y coordinate.) Use sine and cosine of reference angles to develop coordinates for other quadrants Recognize that co-terminal angles have the same trigonometric function values. F.TF.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. ★ (additional) Ability to recognize graphs of parent functions of trigonometric functions Ability to connect contextual situations to appropriate trigonometric function: e.g. using sine or cosine to model cyclical behavior Relate transformations of other functions to trigonometric functions to highlight amplitude (vertical stretch or compression), period (horizontal stretch or compression) and phase shift (horizontal translation), and midline (vertical shift.) Recognize that period and frequency are reciprocals. Recognize that the graphs of sine and cosine functions have an amplitude, while the graphs of other trigonometric functions do not because there is no maximum or minimum value.
A2_UP_U2_Trig_Functions_Jan_3.docx