EXACT TRIG VALUES

• Why is it useful to know the exact values for trigonometric functions?

  It helps in simplifying calculations and recognizing cancellations in problems.
• What is the value of the sine of 0 degrees?

  0
• What is the value of the sine of 30 degrees?

  0.5
• What is the value of the sine of 45 degrees?

  $\frac{\sqrt{2}}{2}$
• What is the value of the sine of 60 degrees?

  $\frac{\sqrt{3}}{2}$
• What is the value of the sine of 90 degrees?


  1
• What is the value of the cosine of 0 degrees?

  1
• What is the value of the cosine of 30 degrees?

  $\frac{\sqrt{3}}{2}$
• What is the value of the cosine of 45 degrees?

  $\frac{\sqrt{2}}{2}$
• What is the value of the cosine of 60 degrees?

  0.5
• What is the value of the cosine of 90 degrees?


  0
• What is the value of the tangent of 0 degrees?

  0
• What is the value of the tangent of 30 degrees?

  $\frac{1}{\sqrt{3}}$
• What is the value of the tangent of 45 degrees?

  1
• What is the value of the tangent of 60 degrees?

  $\sqrt{3}$
• What is the value of the tangent of 90 degrees?


  undefined
• What is a quick method to remember the exact values of trigonometric functions?

  • Start with sine of 0 = 0
  • Write down 1, 2, 3, 4 and 4, 3, 2, 1, 0
  • Take the square root of each and divide by 2
  • This gives sine values for 0, 30, 45, 60, and 90 degrees
• How do the exact trigonometric values in degrees relate to radians?

  • The values are the same for corresponding angles.
  • 0° = 0 radians
  • 30° = $\frac{\pi}{6}$
  • 45° = $\frac{\pi}{4}$
  • 60° = $\frac{\pi}{3}$
  • 90° = $\frac{\pi}{2}$
• How can you derive the tangent values from sine and cosine values?

  By dividing the sine value by the cosine value for the same angle.
• What happens to the tangent value at 90 degrees?

  It becomes undefined due to division by zero.
• What is the sine of $\frac{\pi}{6}$?


  0.5
• What is the sine of $\frac{\pi}{4}$?


  $\frac{\sqrt{2}}{2}$
• What is the sine of $\frac{\pi}{3}$?


  $\frac{\sqrt{3}}{2}$
• What is the cosine of $\frac{\pi}{6}$?


  $\frac{\sqrt{3}}{2}$
• What is the cosine of $\frac{\pi}{4}$?


  $\frac{\sqrt{2}}{2}$
• What is the cosine of $\frac{\pi}{3}$?


  0.5
• What is the cosine of $\frac{\pi}{2}$?


  0