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Category: Trignometry

Use a half angle identity to find the exact value- sin(75 degrees)

Friday, July 23rd, 2010

Solution:

The line of a half angle identity is as follows:

If we plug in 75 degrees we get:

Find the descriminant of x^2-7x+2=0 and describe the natural roots

Friday, July 23rd, 2010

Solution:

  1. When you have an equation in the form of ax2 + =x + c = 0, the solution is x = where  D = b2 – 4ac
  2. D stands for discriminant, and values of x are the natural roots
  • If D > 0, then the values of x are real and distinct.
  • If D = 0, then the values of x are real and equal
  • If D < 0, then the values of x are unreal
  1. In your question, x2 – 7x + 2 = 0, so the values of a, b and c are as follows:
  • a = 1
  • b = -7
  • c = 2
  1. D = b2 – 4ac = 49 – 8 = 41 (this is the value of the discriminant)
  2. Since D > 0, then the values of x (the natural roots) are real and distinct