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Today you will use shifts and vertical stretches to graph and find the equations of sinusoidal functions. You will also learn the 5-point method for sketching graphs. What does the “normal” sine graph look like? What does the “normal” cosine graph look like? Sine Wave Tracer Draw the “normal” graph for each. Label the 5 key points. Maximum? Minimum? Crossings? Period? Amplitude? Parent Equation General Equation P arent E quation: y sin x G eneral E quation: y a sin( b ( x c )) d Period: 2π Amplitude: 1 Maximum: ( Minimum: ( ,1) 2 3 , 1) 2 Crossings: (0, 0) ( , 0) (2 , 0) P arent E quation: y cos x G eneral E quation: y a cos( b ( x c )) d Period: 2π Amplitude: 1 Maximum: (0,1) and (2 ,1) Minimum: Crossings: ( , 1) ( 2 , 0) ( 3 2 , 0) Reflect over x-axis y A sin B x C D Vertical Stretch/ Shrink Left/ Right Up/Down Horizontal Stretch/ Shrink Complete 4-49 & 4-50 with your partner. Complete 4-52 parts b, c, and d with your partner. Use the 5-point method to help you sketch the graph for the function that was given to you. HW 4.1.4 4-53 to 4-61 (pg. 197)