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How To Graph Sine and Cosine F07

# How To Graph Sine and Cosine F07 - 6 3π 2 π 4 2π 2π 4 1...

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Trig F07 O’Brien How to Graph d c) (bx a y + - = sin and d c) - (bx a y + = cos 1. Identify a, b, c, and d. 2a. Find the amplitude: amp = |a|. b. Determine if there has been an x-axis reflection: if a is negative, there has been an x-axis reflection. 3a. Find the period: period = b . b. Find the x-increment: x-increment = period 4 1 . 4. Find the phase shift by setting the argument, bx – c, equal to zero and solving for x: P.S. = b c right (if we see bx – c and b c is positive) or P.S. = b c left (if we see bx + c and b c is negative). 5. Find the vertical shift: |d| up if d is positive or |d| down if d is negative. 6. Identify the five key points: for sine : d b c , (x 1 + x-inc, d+a) (x 2 + x-inc, d) (x 3 + x-inc, d – a) (x 4 + x-inc, d) for cosine : + a d b c , (x 1 + x-inc, d) (x 2 + x-inc, d – a) (x 3 + x-inc, d) (x 4 + x-inc, d + a) 7. Plot the five key points and connect them with a smooth, continuous curve, then extend the graph to two full periods. Example 1: 1 3 π x sin 2 y + - - = 1. a = –2 b = 1 c = 3 π d = 1 2. amp = |–2| = 2 There is an x-axis reflection. 3. period = 2π x-increment =

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Unformatted text preview: 6 3π 2 π 4 2π 2π 4 1 = = = ⋅ Note: To make graphing the phase shift easier, we will use an x-increment of 6 π . 4. phase shift = 6 2π or 3 π right 6 2π 3 π x 3 π x = = → =-5. vertical shift = 1 up 6. 5 key points: 1 , 6 2π 1-, 6 5π 1 , 6 8π 3 , 6 11π 1 , 6 14π 7. 1 Trig F07 O’Brien Example 2: y = 3 1 cos (4x + π) – 2 1. a = 3 1 b = 4 c = –π d = –2 = – 3 6 2. amp = 3 1 = 3 1 There is no x-axis reflection. 3. period = 2 π 4 2π = x-increment = 8 π 2 π 4 1 = ⋅ 4. phase shift = 4 π or 8 2π left 8 2π 4 π x π 4x π 4x-=-= →-= → = + 5. vertical shift = 2 or 3 6 down 6. 5 key points: --3 5 8 2π , --3 6 8 π , -3 7 , -3 6 8 π , -3 5 8 2π , 7. 2...
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How To Graph Sine and Cosine F07 - 6 3π 2 π 4 2π 2π 4 1...

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