Trigonometric graphs

• What are the three trigonometric graphs to know?

  y = sin of X, y = cos of X, y = tan of X
• What is the range of x values typically used for sketching trigonometric graphs?

  0 to 360 degrees
• What are the key points to mark when sketching the graph of y = sin of X?

  • (0, 0)
  • (90, 1)
  • (180, 0)
  • (270, -1)
  • (360, 0)
• What is the maximum value of y = sin of X?

  1
• What is the minimum value of y = sin of X?

  -1
• What does sin(0) equal?

  0
• What does sin(90) equal?

  1
• What does sin(180) equal?

  0
• What does sin(270) equal?

  -1
• What does sin(360) equal?

  0
• What is the value of sin(30)?

  0.5
• What is the value of sin(45)?

  $\frac{\sqrt{2}}{2}$
• What is the value of sin(60)?

  $\frac{\sqrt{3}}{2}$
• What are the key points to mark when sketching the graph of y = cos of X?

  • (0, 1)
  • (90, 0)
  • (180, -1)
  • (270, 0)
  • (360, 1)
• What does cos(0) equal?

  1
• What does cos(90) equal?

  0
• What does cos(180) equal?

  -1
• What does cos(270) equal?

  0
• What does cos(360) equal?

  1
• What is the value of cos(30)?

  $\frac{\sqrt{3}}{2}$
• What is the value of cos(45)?

  $\frac{\sqrt{2}}{2}$
• What is the value of cos(60)?

  0.5
• How do the graphs of y = sin of X and y = cos of X compare?

  • Same shape
  • Cosine graph is a 90° shift of sine graph
• What are the characteristics of the graph of y = tan of X?

  • Periodic with a period of 180°
  • Has vertical asymptotes at 90° and 270°
  • Takes any possible y value
• What is the period of the graph of y = tan of X?

  180 degrees
• What does tan(90) equal?

  Undefined
• What does tan(180) equal?

  0
• What does tan(360) equal?

  0
• What is the periodic nature of the graphs of y = sin of X and y = cos of X?

  • Both are periodic
  • Period is 360°
• What is the periodic nature of the graph of y = tan of X?

  • Periodic with a period of 180°
  • Repeats infinitely in both directions
• How do you estimate solutions for sin(x) = 0.6 using the graph?

  Draw a horizontal line at 0.6
• What are the x values where sin(x) = 0.6?

  36 and 144 degrees
• How do you estimate solutions for sin(x) = 0.9 using the graph?

  Draw a horizontal line at 0.9
• What are the x values where sin(x) = 0.9?

  246 and 294 degrees
• How do you estimate solutions for cos(x) = 0.3 using the graph?

  Draw a horizontal line at 0.3
• What are the x values where cos(x) = 0.3?

  72 and 288 degrees
• How do you estimate solutions for cos(x) = 0.4 using the graph?

  Draw a horizontal line at 0.4
• What are the x values where cos(x) = 0.4?

  114 and 246 degrees
• What should you do when solving equations using trigonometric graphs?

  • Draw horizontal lines at the given y value
  • Identify intersection points with the graph
  • Read corresponding x values from the x-axis
• What are the two values found when drawing lines back to the x-axis for the first part of the problem?

  240 and 294