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Reflective Portfolio Unit #9: Trigonometry Section #1: Vocabulary (words and/or diagrams) Define each: Use words or a LABELED diagram. Acute angle Angle in standard position Initial side Terminal side Co-terminal angle Reference angle Periodic function Quadrantal angle Reference Triangle Radian Sinusoidal graphs Amplitude period frequency midline vertical shift Section #2: Formulas/Equations/Rules Draw and label the Special Right Triangle Ratios (45-45-90, 30-60-90) State the Pythagorean TRIG identity: Number the quadrants Label the signs of an ordered pair in each quadrant State the 3 basic trig functions and their corresponding Reciprocal Functions Basic trig functions Reciprocal trig functions In the unit circle, the cosine is the ____-coordinate, the sine is the _____-coordinate and the tangent is what quotient in terms of cos and sin? s r where s represent the __________ _____________, ___________ in ______________, and r represents the _____________ represents the ___________________. 1) How long (in terms of pi) is the arc subtended by an angle of cm? radians on a circle of radius 40 2) A central angle of a circular garden measures 120 degrees and intercepts an arc of 90 feet. What is the radius of the garden measured to the nearest foot? Section #3: Key methods and concepts Find a positive and negative co-terminal angle for each: a) 135º b) 330º c) 4 c) 4 Find the ordered pair that lies on the unit circle for each angle: Draw the reference triangle for each!!!! a) 135º b) 330º How to find the exact value of a trigonometric function o Include the following examples: (notice the work is done above.) a) cos 135º b) csc 330º c) tan 4 How to convert radians to degrees o Include this example: Convert 5 to degrees 3 How to convert degrees to radians o Include this example: Convert 315o to radians If sin 3 and 270 360 , find the exact value of the other 5 trigonometric functions. 5 Trig Graphs to know y=sin(x) y=cos(x) What is the difference between the graph of the sine function and the graph of the cosine function? Graph the following: y= -2cos(x)+1 amplitude=_____ frequency=____ period=______ vertical shift:_____ midline=________ Trig Graphs: Apply to real-life 1) (trig equation) a sine graph with the following parameters amplitude=__2__ period=___π___ midline: y 1