trigonometry graphs

• Characteristic of a Sine Graph?

  Wave-like shape, periodic, and oscillates between positive and negative values
• What is the range of the Sine Function?

  [-1, 1]
• Is the Sine Function odd?

  Yes, sin(-x) = -sin(x)
• Characteristic of a Cosine Graph?

  Shifted sine graph, same period but with phase shift
• What is the range of the Cosine Function?

  [-1, 1]
• Is the Cosine Function even?


  Yes, cos(-x) = cos(x)
• Difference between Cosine and Sine?

  Even/odd functions, phase shift, domain and range, graph properties
• Is the Cosine Function even?


  Yes
• Does the Sine Function have a phase shift?


  No
• Where do Sine and Cosine Graphs intersect?

  At the origin, where sin(x) = cos(x) = 0
• Characteristic of a Tangent Graph?

  Jagged, oscillating curve with vertical asymptotes at odd multiples of π/2
• What happens to the Tangent Function at odd multiples of π/2?


  It is undefined and has an infinite slope
• Why do the Tangent Graphs have Vertical Asymptotes?

  Because the Tangent Function is undefined at odd multiples of π/2, causing a singularity
• Why is the Tangent Function undefined at odd multiples of π/2?

  Because the adjacent side becomes zero, making the ratio undefined
• Phase Shift on Graph

  A phase shift shifts the graph along the x-axis without changing its shape or period
• Phase Shift Visualization

  Phase shift is like moving a party to a new location, maintaining the same shape, amplitude, and period, but changing the starting point