WARM UP 2 2 3 2 1 1

WARM UP 2, 2, 3, 2, 1, 1

Angle Sin Cos Tan Csc Sec Cot 0 0 1 0 Undef 1 Undef 2 1 1 2 1 0 Undef 1 Undef 0 -2 -1 -1 2 0 -1 0 Undef -1 Undef -2 1 1 -2 -1 0 Undef -1 Undef 0 2 -1 -1 -2 0 1 0 Undef 1 Undef

8. 2 SINE AND COSINE CURVES Objective: To find equations of different sine and cosine curves and to apply these equations

Trig Curves Transformed Graph Sine & Cosine Functions

VARIATIONS OF THE BASIC GRAPHS We are interested in the graphs of functions in the form y = A sin B (x – h) + k and y = A cos B (x – h) + k where A, B, h, and k are all constants. These constants have the effect of translating, reflecting, stretching, and shrinking the basic graphs.

y = A sin B (x – h) + k and y = A cos B (x – h) + k Copyright © 2009 Pearson Education, Inc.

Equation of a Sine Function Amplitude Period Complete Cycle

Draw one cycle of the function’s graph. Amplitude Period

Draw one cycle of the function’s graph. Amplitude Period

Draw one cycle of the function’s graph. Amplitude Period

Equation of a Cosine Function Amplitude Period Complete Cycle

Draw one cycle of the function’s graph. Amplitude Period

Draw one cycle of the function’s graph. Amplitude Period

Draw one cycle of the function’s graph. Amplitude Period

Graph the function. Amplitude Period Reflection over x-axis

Graph the function. Amplitude Period Reflection over x-axis

Phase Shift Vertical Displacement Reflection Vertical Stretch/Shrink Horizontal Stretch/Shrink Stretches/shrinks the “wiggle” of the tangent curve

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