Unit Plan 1: Triangle Trig and Circles 3 weeks (7 days?)MA: Funct.,Trigonometric FunctionsF-TF Extend the domain of trigonometric functions using the unit circle. 1. Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle. 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. 3. (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for /3, /4 and /6, and use the unit circle to express the values of sine, cosines, and tangent for x, + x, and 2 x in terms of their values for x, where x is any real number. using the unit circle to solve problems using the calculator to solve problems Construct a unit circleApply given information of a circle to find the missing piece(s). Convert between radians and degrees.

Key Terms:Radian: a new unit of measurement for angles. 1 radian has an arc of length 1 radius. Radians=arc/radiusSecant: the reciprocal of cosineCosecantCotangent

Day 1Survey - Draw an accurate circle graph (central angle, arc length)(dont print circles or theyll all have the same radius for day 3)Day 2As the World Turns (angular vs. linear speed)Day 3Quiz: arc length/central angleGo back to circle graph, measure with the fancy new (decimal radian) protractors. Find a way to relate radius, arc length and these new things. (radian=arc/radius)Applet of radii being placed along circumference http://www.geogebratube.org/student/m59882 Determine the number of degrees and radians a figure skater rotates for each jump:a) single axel, 1.5 revolutionsb) double axel, 2.5 revolutionsc) triple axel, 3.5 revolutionsMake a diagram for each (coterminal angles)Day 4Comment by Salem Public Schools: Great to go over HW on converting with linear/angular speed then intro radians conversion factors fresh!Graph anglesConvert between radians and degreesAngle Races use polar white boards (build familiarity with radians, practice adding fractions!)Day 5Make lots of triangles with same hypotenuse http://mythagon.wordpress.com/2014/05/15/thinking-about-folding/ (build unit circle by lining them all up on the x axis)Use special right triangles to fill in unit circle (radians, degrees, exact values)Day 6Quiz: convert between radians and degreesReference anglesCoterminalUse chart labeled as HW start in class finish for HWDay 7Practice finding cos, sin -> x and y coordinates All 6 trig functions from unit circleDay 8 (short day)Unit Circle ProjectDay 9Continue Unit Circle ProjectAll 6 inverse trig functions from unit circle (within a certain range)Day 10Quiz: label parts of circle (on radian, one degree, one coordinate)ReviewFirst opportunity to fill in a unit circle completely by memory (if perfect stamp it and they can use it on all future assessments)Day 11TestGiven a point (not on unit circle), find the ratio