# Thread: Homework Help

1. ## Homework Help

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

1. Consider the circle given by $x^{2}+y^{2}=1$. 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 $\Theta$ has a terminal arm in the third quadrant. If $\cot\theta = \frac{12}{5}$, find the values of the remaining five primary and reciprocal trigonometric ratios.

Thank you for all your help in advance!

2. ## Re: Homework Help

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)

3. ## Re: Homework Help

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