Homework Help

A couple more questions giving me problems in my homework, please be very explanatory! :)

1. Consider the circle given by http://latex.codecogs.com/gif.latex?...+y%5E%7B2%7D=1. Determine the equation of the transformed function if the graph undergoes a horizontal stretch by a factor of 1/2, vertical stretch by a factor of 3, horizontal translation of 1 unit right and a vertical translation 4 units down.

2. Angle http://latex.codecogs.com/gif.latex?%5CTheta has a terminal arm in the third quadrant. If http://latex.codecogs.com/gif.latex?...7B12%7D%7B5%7D, find the values of the remaining five primary and reciprocal trigonometric ratios.

Thank you for all your help in advance!

Write it as y^2=1-x^2
Learn the following steps because they would apply whatever the question.
1 Replace x by 2x (so x^2 becomes (2x)^2=4x^2
2 We need the 3 times the expression for y ( so y^2 will get multiplied by 9)
3 Replace x by (x-1)
4 Replace y by (y+4)

In the 3rd quadrant tan and therefore cot are positive, sin and cosec are negative, cos and sec are negative. I'll write x instead of theta.
cotx=12/5 so tanx=5/12
sec^2x=1+tan^2x=1+25/144=169/144 So secx =+or-13/12 We know in 3rd quadrant it is negative. So secx=-13/12 and cosx=-12/13
sin^2x=1-cos^2x=1-144/169=25/169 So sinx=+or-5/13 In 3rd quadrant is - So sinx=-5/13 and cosecx=-13/5