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Test Preperation NEED HELP

  1. Feb 25, 2012 #1
    I'm currently working through a self taught program, coming up to my first test and have found a review that works well for what I need, I'm stuck on several questions and any help you can provide on any of them will greatly help!

    1. Consider the function: y = x^2 - 2x - 8
    a) State the equation of the reciprocal function
    b) Write the equation of the vertical asymptotes (I find this to be a parabola which can't have asymptotes which is my struggle)

    2. If "a" is an angle in Quadrant 4 where cos a = 4/5, and "b" in an angle with sinb= 12/13 where 90 degrees< b < 180 degrees.
    a) What is the exact value of sin(a+b)?

    Any help you can provide or links to pages or videos will greatly help! Thank you!
     
  2. jcsd
  3. Feb 25, 2012 #2
    2a:

    Expanding sin(a+b) gives sin(a)cos(b) + cos(a)sin(b). So we need to find cos(b) and sin(a).

    Since angle a is in quadrant 4, sin(a) is negative. So it is [itex]-\sqrt{1 - \left(\frac{4}{5}\right)^2}[/itex], or -1/5.

    Since angle b is in quadrant 2, cos(b) is negative. So it is [itex]-\sqrt{1 - \left(\frac{12}{13}\right)^2}[/itex], or -5/13.

    Simplifying sin(a+b) gives [itex]-\frac{1}{5} \cdot -\frac{5}{13} + \frac{4}{5} \cdot \frac{12}{13}[/itex], or [itex]\boxed{\frac{53}{65}}[/itex].
     
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