CDs would now cost $12.60. And cassettes would now be $9
Answer:
![$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$](https://tex.z-dn.net/?f=%24%5Ccsc%20%5Cleft%28%5Ctheta-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%3D0.73%24)
Step-by-step explanation:
The identity you will use is:
![$\csc \left(x\right)=\frac{1}{\sin \left(x\right)}$](https://tex.z-dn.net/?f=%24%5Ccsc%20%5Cleft%28x%5Cright%29%3D%5Cfrac%7B1%7D%7B%5Csin%20%5Cleft%28x%5Cright%29%7D%24)
So,
![$\csc \left(\theta-\frac{\pi }{2}\right)$](https://tex.z-dn.net/?f=%24%5Ccsc%20%5Cleft%28%5Ctheta-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%24)
![$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{\sin \left(-\frac{\pi }{2}+\theta\right)}$](https://tex.z-dn.net/?f=%24%5Ccsc%20%5Cleft%28%5Ctheta-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%3D%5Cfrac%7B1%7D%7B%5Csin%20%5Cleft%28-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%2B%5Ctheta%5Cright%29%7D%24)
Now, using the difference of sin
Note: state that ![\text{sin}(\alpha\pm \beta)=\text{sin}(\alpha) \text{cos}(\beta) \pm \text{cos}(\alpha) \text{sin}(\beta)](https://tex.z-dn.net/?f=%5Ctext%7Bsin%7D%28%5Calpha%5Cpm%20%5Cbeta%29%3D%5Ctext%7Bsin%7D%28%5Calpha%29%20%5Ctext%7Bcos%7D%28%5Cbeta%29%20%5Cpm%20%5Ctext%7Bcos%7D%28%5Calpha%29%20%5Ctext%7Bsin%7D%28%5Cbeta%29)
![$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)}$](https://tex.z-dn.net/?f=%24%5Ccsc%20%5Cleft%28%5Ctheta-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%3D%5Cfrac%7B1%7D%7B-%5Ccos%20%5Cleft%28%5Ctheta%5Cright%29%5Csin%20%5Cleft%28%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%2B%5Ccos%20%5Cleft%28%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%5Csin%20%5Cleft%28%5Ctheta%5Cright%29%7D%24)
Solving the difference of sin:
![$-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)$](https://tex.z-dn.net/?f=%24-%5Ccos%20%5Cleft%28%5Ctheta%5Cright%29%5Csin%20%5Cleft%28%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%2B%5Ccos%20%5Cleft%28%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%5Csin%20%5Cleft%28%5Ctheta%5Cright%29%24)
![-\cos \left(\theta\right) \cdot 1+0\cdot \sin \left(\theta\right)](https://tex.z-dn.net/?f=-%5Ccos%20%5Cleft%28%5Ctheta%5Cright%29%20%5Ccdot%201%2B0%5Ccdot%20%5Csin%20%5Cleft%28%5Ctheta%5Cright%29)
![-\text{cos} \left(\theta\right)](https://tex.z-dn.net/?f=-%5Ctext%7Bcos%7D%20%5Cleft%28%5Ctheta%5Cright%29)
Then,
![$\csc \left(\theta-\frac{\pi }{2}\right)=-\frac{1}{\cos \left(\theta\right)}$](https://tex.z-dn.net/?f=%24%5Ccsc%20%5Cleft%28%5Ctheta-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%3D-%5Cfrac%7B1%7D%7B%5Ccos%20%5Cleft%28%5Ctheta%5Cright%29%7D%24)
Once
![\text{sec}(-\theta)=\text{sec}(\theta)](https://tex.z-dn.net/?f=%5Ctext%7Bsec%7D%28-%5Ctheta%29%3D%5Ctext%7Bsec%7D%28%5Ctheta%29)
And,
![$-\frac{1}{\cos \left(\theta\right)}=-\text{sec}(\theta)$](https://tex.z-dn.net/?f=%24-%5Cfrac%7B1%7D%7B%5Ccos%20%5Cleft%28%5Ctheta%5Cright%29%7D%3D-%5Ctext%7Bsec%7D%28%5Ctheta%29%24)
![$-\frac{1}{\cos \left(\theta\right)}=-(-0.73)$](https://tex.z-dn.net/?f=%24-%5Cfrac%7B1%7D%7B%5Ccos%20%5Cleft%28%5Ctheta%5Cright%29%7D%3D-%28-0.73%29%24)
![$-\frac{1}{\cos \left(\theta\right)}=0.73$](https://tex.z-dn.net/?f=%24-%5Cfrac%7B1%7D%7B%5Ccos%20%5Cleft%28%5Ctheta%5Cright%29%7D%3D0.73%24)
Therefore,
![$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$](https://tex.z-dn.net/?f=%24%5Ccsc%20%5Cleft%28%5Ctheta-%5Cfrac%7B%5Cpi%20%7D%7B2%7D%5Cright%29%3D0.73%24)
Answer : I need a graph or something
Answer:
4320
Step-by-step explanation:
multiply 6% by 18(One year/12 months + Half of a year/6) you will get 1.08. Then take that and multiply that by 4000. You should get 4320