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5.3 Properties of the Trigonometric Functions Objectives: • Identify the signs of trig functions for each quadrant • Find the exact values of the Trig Functions of an angle given: one function and the quadrant. Title: Feb 26 ­ 9:15 PM (1 of 10) Periodic Functions Because our trigonometric functions continue infinitely, but repeat their values they are called periodic functions. Each revolution yields the same values for sine and cosine and their cofunctions. Title: Feb 26 ­ 10:05 PM (2 of 10) Find the exact value of the following trigonometric functions. Title: Feb 26 ­ 10:13 PM (3 of 10) Signs of your function depend on which quadrant you are in. cosine is negative sine is positive cosine is negative sine is negative Title: Feb 26 ­ 10:18 PM (4 of 10) cosine is positive sine is positive (­ , +) (+ , +) (­ , ­) (+ , ­) cosine is positive sine is negative Name the quadrant in which the angle θ lies. 1. sin θ > 0, cos θ < 0 2. sin θ < 0, tan θ < 0 3. cos θ > 0, tan θ < 0 Title: Feb 26­11:34 AM (5 of 10) Finding the exact values of a trigonometric function. 12 5 Given that sin = and cos = , find the exact values of each 13 13 of the remaining trigonometric functions. step 1: Identify what information is given and what needs to be discovered = opp hyp opp = 12 = adj = 5 adj hyp hyp = 13 step 2: Using this information, find the remaining trigonometric functions = csc = Title: Feb 27 ­ 7:02 AM (6 of 10) sec = cot = Finding the exact values of a trigonometric function. , find the exact values of each of Ex. 1 Given that the remaining five trigonometric functions. Step 1: Determine the Quadrant the P(x,y) is in. Step 2: Draw a triangle in the appropriate quadrant. Step 3: Identify the given values x, y, or r. Find the value of x. Title: Feb 27 ­ 7:02 AM (7 of 10) Step 4: Find the remaining trigonometric values. Title: Feb 27 ­ 9:13 AM (8 of 10) Ex. 2 Given that find the other trig functions. Title: Feb 27 ­ 8:26 PM (9 of 10) HOMEWORK: page 399 (12 ­ 42 even) Title: Feb 26­11:38 AM (10 of 10)