Improve Your Test Preparation with Expert Help - Math Questions Solved

[Prents]

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!

 

[professordad]

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 $-\sqrt{1 - \left(\frac{4}{5}\right)^2}$, or -1/5.

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

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