A function f is odd if and only if f(x) 52f(2x) for all x in the domain of the

Chapter 11, Problem 9

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A function f is odd if and only if f(x) 52f(2x) for all x in the domain of the function.Note that a function is odd if it is symmetric with respect to the origin.In other words,the function is its own image under a reflection about the origin.a. Draw a unit circle and any first-quadrant angle ROP in standard position,with point P on the unit circle.Let mROP 5u . b. On the same set of axes,draw an angle in standard position with measure 2u.What is the relationship between u and 2u? Between sin u and sin (2u)? c. Repeat steps a and b for second-,third-,and fourth-quadrant angles.Does sin u5sin (2u) for second-,third-,and fourth-quadrant angles? Justify your answer. d. Does sin u52sin (2u) for quadrantal angles? Explain. e. Do parts ad show that y 5 sin x is an odd function? Justify your answer.