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Warm-up Graph the following and find the amplitude, period, increment, S.A., starting point, domain and range. Y = -2sin(2x + 4π) – 1

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4.4 Tangent and Cotangent

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TAN people M ight H ate A pplying L otion

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A ll H ail the M ath L etes

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Let’s do two together y = 2tan(2x – π) – 1 y = -2tan(2x – π) – 1

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Steps to Graphing Tangent and Cotangent (y=a*tan(bx-c)+d) 1) Find phase shift by setting bx - c = 0 and solving for x. 2) Find period π/b and increment period/4. Mark off starting point and increments on the x-axis. 3) Use d and a to find the Middle point (y = d), High point (y = d +|a|), Low point (y = d - |a|). 4) Plot points using MHAL or AHML depending on if its tangent or cotangent respectively. Vertically flip graph if the leading coefficient a is negative. 5) Connect the points L,M and H with smooth curves and draw vertical dashed lines through A for the asymptotes.

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Guided Practice/HW y = -3tan(πx - 4 ) + 3 Y = 4tan(πx/4) – 2 Y= -4tan(πx/2 + π/2) + 2 Y =cot(2x) Graph each trig function and find the amplitude, period, increment, S.A., starting point, domain and range.

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Guided Practice/HW y = -3tan(πx - 4 π) + 3 Y = 4tan(πx/4) – 2 Y= -4tan(πx/2 + π/2) + 2 Y =cot(2x) Y = 3cot(x – π/2) + 2 Y = -2cot(2x + π) – 3 Y = (-1/2)tan(4x – π) + 1 Y = 3tan(πx + 2 π) - 3 Graph each trig function and find the amplitude, period, increment, S.A., starting point, domain and range.

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Sine and Cosine Review Y = 3sin(2x) + 1 Y = 4cos(x/2) + 1 Y = - 3cos(πx - 2π) + 1

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Warm up Find the values of θ for which cot θ = 1 is true. Write the equation for a tangent function whose period is 4π, phase shift 0, and vertical shift.

Warm up Find the values of θ for which cot θ = 1 is true. Write the equation for a tangent function whose period is 4π, phase shift 0, and vertical shift.

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