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Graphs of the Tangent

Graphs of the Tangent. Precalculus 2. Agenda . SWBAT:. Accurately sketch a SINE, COSINE And TANGENT transformation, ID-ing amplitude, period, horizontal and vertical shifts!!. Do Now: Whattaya Remember about PEMDAS and RADicals?

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Graphs of the Tangent

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  1. Graphs of the Tangent

  2. Precalculus 2 Agenda SWBAT: Accurately sketch a SINE, COSINE And TANGENT transformation, ID-ing amplitude, period, horizontal and vertical shifts!! • Do Now: Whattaya Remember about PEMDAS and RADicals? • CW: Work on Portfolio! Yes, YOU NEED To be able to graph sine, cosine and tangent • HW: UNIT Exam TUESDAY and WEDNESDAY!!

  3. Precalculus 1 and 2 Agenda SWBAT: Review Geometry for MCAS Accurately sketch a SINE, COSINE And TANGENT transformation, ID-ing amplitude, period, horizontal and vertical shifts!! • Do Now: Write the COSINE transformations! • Class work – Geometry MCAS Review! • HW: Review ALL Sine and Cosine Packets…remember our Unit Exam is THURSDAY!!!!

  4. The Graph of y = tan x y x

  5. (0, 0)

  6. What happens as x approaches ? ….it’s UNDEFINED!! What happens as x approaches ? ….it’s UNDEFINED!!!

  7. This is the graph for y = tan x. y = - tan x Consider the graph for y = - tan x In this equation a, the numerical coefficient for the tangent, is equal to -1. The fact that a is negative causes the graph to “flip” or reflect about the x-axis.

  8. y = a tanb (x - h)+k b affects the period of the tangent graph. For tangent graphs, the period can be determined by Conversely, when you already know the period of a tangent or cotangent graph, b can be determined by

  9. For all tangent graphs, the period is equal to the distance between any two consecutive vertical asymptotes. The distance between the asymptotes in this graph is… Therefore, the period of this graph is also .

  10. y = tan x has no phase shift. We designated the y-intercept, located at (0,0), as the key point.

  11. It is important to be able to draw a tangent graph when you are given the corresponding equation. Consider the equation Begin by looking at a, b, and c.

  12. The negative sign here means that the tangent graph reflects or “flips” about the x-axis. The graph will look like this.

  13. b = 3 Use bto calculate the period. Remember that the period is the distance between vertical asymptotes.

  14. This phase shift means the key point has shifted spaces to the right. It’s x-coordinate is . Also, notice that the key point is an x-intercept.

  15. The distance between the x-intercept and the asymptotes on either side is , because it is half the period!!!! Caution: the distance to the asymptotes will not always be the same as the phase shift.

  16. Vertical asymptote X-intercept

  17. Continue to add or subtract half of the period, , to determine the labels for additional x-intercepts and vertical asymptotes. x-intercept Vertical asymptote

  18. http://www.analyzemath.com/Tangent/Tangent.html

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