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Graphs of Trigonometric Functions Graphing Other Trigonometric Functions Properties of Trigonometric Graphs • 1. 2. 3. 4. 5. 6. 7. 8. When graphing a trigonometric function you need to be able to identify the properties of the graph. Period Amplitude Domain Range X intercepts (if any) Y intercept (if any) Maximum and minimum points (if any) Asymptotes (if any) Tangent Function y • Remember tan θ = . Tangent is x undefined at 90 degrees, 270 degrees, negative 90 degrees, etc. It is undefined for any multiple of 90 degrees. • Therefore it has asymptotes at these points. Thus it’s domain is the set of real numbers except for these points. • Also tangent and cotangent have a period of π whereas the other four trigonometric functions have a period of 2π Properties From the video, we can now state the properties of the graph y = tan x 1. Period is π 2. Domain: Set of all real numbers except π 2 n where n is an odd integer. 3. Range: Set of all real numbers 4. X intercepts are located at 5. The y intercept is 0 6. The asymptotes are odd integer. πn x= where n is an integer. π 2 n where n is an Reciprocal Relationship • The sine and cosecant functions are reciprocal functions. • The cosine and secant functions are reciprocal functions • The tangent and cotangent functions are reciprocal functions. Cosecant • Let’s look at another video and determine the graph of cosecant, the reciprocal of sine. Period Formula • The period of functions y = sin kθ , y = cos kθ , y = sec kθ , y = csc kθ 2π is , where k > 0 k • The period of functions y = tan kθ and y = cot kθ is π k where k > 0 HW # 48 • Section 6-7 • Pp. 400-403 • # 8, 9, 29, 30, 31, • 33, 37, 39, 52, 54 Work with your partner * Find each value by referring to the graphs of the trigonometric functions. 1. Tan 7π/2 2. cot 3π/2 3. Write an equation for a secant function with a period of 3π , phase shift π/2 , and vertical shift 3. Find the values of x for which each equation is true. 4. csc x = 1 5. sec x = 1 6. Graph y = csc (2θ – π/2) + 1 (Hint: make the vertical shift first)