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M1410405Part1 - 4.33 SECTION 4.5 GRAPHS OF SINE AND COSINE...

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4.33 SECTION 4.5: GRAPHS OF SINE AND COSINE FUNCTIONS PART A : GRAPH f θ ( ) = sin θ Note: We will use θ and f θ ( ) for now, because we would like to reserve x and y for discussions regarding the Unit Circle. We use radian measure (i.e., real numbers) when we graph trig functions. To analyze sin θ , begin by tracing the y -coordinate of the blue intersection point as θ increases from 0 to 2 π .
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4.34 We obtain one cycle of the graph of f θ ( ) = sin θ . A cycle is the smallest part of a graph (on some interval) whose repetition yields the entire graph. Because such a cycle can be found, f is called a periodic function. The period of f θ ( ) = sin θ is 2 π . This is because coterminal angles have the same basic trig values (Think: Retracing the Unit Circle), and the y -coordinate of the blue intersection point never exhibits the same behavior twice on the θ -interval 0, 2 π ) . To construct the entire graph of f θ ( ) = sin θ , draw one cycle every 2 π units along the θ -axis. “Framing” One Cycle (Inspired by Tom Teegarden) (enlarged on the next page ) We can use a frame to graph one or more cycles of the graph of f θ ( ) = sin θ , including the cycle from θ = 0 to θ = 2 π . The five “key points” on the graph that lie on the gridlines correspond to the maximum points, the minimum points, and the “midpoints” (here, the θ -intercepts). The midpoints may also be thought of as
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