First lets see the pythagorean identities
![sin^2 \Theta + cos^2 \Theta =1](https://tex.z-dn.net/?f=%20sin%5E2%20%5CTheta%20%2B%20cos%5E2%20%5CTheta%20%3D1%20)
So if we have to solve for sin theta , first we move cos theta to left side and then take square root to both sides, that is
![sin^2 \Theta = 1-cos^2 \Theta => sin \theta = \pm \sqrt{1-cos^2 \Theta}](https://tex.z-dn.net/?f=%20sin%5E2%20%5CTheta%20%3D%201-cos%5E2%20%5CTheta%20%3D%3E%20sin%20%5Ctheta%20%3D%20%5Cpm%20%5Csqrt%7B1-cos%5E2%20%5CTheta%7D%20)
Now we need to check the sign of sin theta
First we have to remember the sign of sin, cos , tan in the quadrants. In first quadrant , all are positive. In second quadrant, only sin and cosine are positive. In third quadrant , only tan and cot are positive and in the last quadrant , only cos and sec are positive.
So if theta is in second quadrant, then we have to positive sign but if theta is in third or fourth quadrant, then we have to use negative sign .
Answer:
x= 1/256
Step-by-step explanation:
1. multiply both sides by 8x (answer: -5= 8x*-160)
2. divide both sides by -160 (answer: -5/-160 or 1/32 =8x)
3. divide both sides by 8 (answer: 1/256 = x
4. check your answer: -5/(8*1/256)= -160
If h moves the graph left or right,
![y= \frac{1}{x+h}](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B1%7D%7Bx%2Bh%7D%20)
(moves left)
![y= \frac{1}{x-h}](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B1%7D%7Bx-h%7D%20)
(moves right)
If a vertical stretch by a factor of |h|, then
![y = \frac{h}{x}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7Bh%7D%7Bx%7D%20)
If h moves the graph up or down,
![y= \frac{1}{x} +h](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B1%7D%7Bx%7D%20%2Bh)
(moves up)
![y= \frac{1}{x} -h](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B1%7D%7Bx%7D%20-h)
(moves down)
![y= \frac{1}{-hx}](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B1%7D%7B-hx%7D%20)
and h = 1