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This review focuses on the fundamentals of sine and cosine graphs, including the essential parameters that define their shapes and behaviors. Key concepts covered include maximum and minimum values, amplitude, period, phase shift, and vertical displacement. The review illustrates how to derive these features from the general equations, y = a sin(b(x – c)) + d and y = a cos(b(x – c)) + d. Understanding these elements is crucial for mastering trigonometric functions and their applications in various mathematical contexts.
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Unit 3 Trigonometry Review Sin & Cos Graphs
y = asin b(x – c) + d y = sin x = 1sin 1(x – 0) + 0 Maximum value = 1 2π π Minimum value = – 1 Amplitude
y = a sin b(x – c) + d y = sin x = 1sin 1(x – 0) + 0 2π π Period =
y = a sin b(x – c) + d y = sin x = 1sin 1(x – 0) + 0 2π π Phase Shift = c = 0
y = a sin b(x – c) + d y = sin x = 1sin 1(x – 0) + 0 2π π Vertical displacement =
y = sin x sin x = 0 0 2π 4π –4π –2π π 3π –π –3π x-intercepts 0 + 2πn, n ε I x-intercepts + 2πn, nε I y-intercept (0, 0)
y = a sin b(x – c) + d max = Period = radians min = Amplitude = Phase Shift = c = a = 2 Vertical displacement = d =
y = a sin b(x – c) + d Period = max = min = Phase Shift = c = Amplitude = a = 3 Vertical displacement = d =
y = a sin b(x – c) + d Period = max = min = Phase Shift = c = Amplitude = a = 3 Vertical displacement = d =
y = a cosb(x – c) + d y = cosx = 1cos 1(x – 0) + 0 Maximum value = 1 Minimum value = – 1 x-intercepts + 2πn, n ε I Amp a = 1 x-intercepts + 2πn, n ε I Period = y-intercept (0, 1) Phase Shift = c = 0 Vertical displacement =
y = a cosb(x – c) + d Period = max = Phase Shift = c = min = Amplitude = a = Vertical displacement = d =
y = a cosb(x – c) + d Period = max = 6 min = Phase Shift = c = Amplitude = a = 5 Vertical displacement = d =
y = 3sin 2(x – ) + 1 a = 3 d = 1 c = Period =
y= 4cos 3(x + ) – 2 Period = c = a = 4 d = – 2
