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Pre-Calc Exam Notes 108

# Pre-Calc Exam Notes 108 - 108 Chapter 5 Graphing and...

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108 Chapter 5 Graphing and Inverse Functions §5.1 It is worthwhile to remember the general shapes of the graphs of the six trigonometric functions, especially for sine, cosine, and tangent. In particular, the graphs of the sine and cosine functions are called sinusoidal curves. Many phenomena in nature exhibit sinusoidal behavior, so recognizing the general shape is important. Example5.2 Draw the graph of y = 1 + cos x for 0 x 2 π . Solution: Adding a constant to a function just moves its graph up or down by that amount, depend- ing on whether the constant is positive or negative, respectively. So adding 1 to cos x moves the graph of y = cos x upward by 1, giving us the graph of y = 1 + cos x : x y 0 1 2 π 4 π 2 3 π 4 π 5 π 4 3 π 2 7 π 4 2 π y = 1 + cos x Exercises For Exercises 1-12, draw the graph of the given function for 0 x 2 π . 1. y =− cos x 2. y = 1 + sin x 3. y = 2 cos x 4. y = 2 sin x 5. y =− tan x 6. y =− cot x 7. y = 1 + sec x 8. y =− 1 csc x 9. y = 2sin x 10. y =− 3cos x 11. y =− 2tan x 12. y
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