Answer:
![a+b-c](https://tex.z-dn.net/?f=a%2Bb-c)
*Note c could be written as a/b
Step-by-step explanation:
-sin(-t - 8 π) + cos(-t - 2 π) + tan(-t - 5 π)
The identities I'm about to apply:
![\sin(a-b)=\sin(a)\cos(b)-\sin(b)\cos(a)](https://tex.z-dn.net/?f=%5Csin%28a-b%29%3D%5Csin%28a%29%5Ccos%28b%29-%5Csin%28b%29%5Ccos%28a%29)
![\cos(a-b)=\cos(a)\cos(b)+\sin(a)\sin(b)](https://tex.z-dn.net/?f=%5Ccos%28a-b%29%3D%5Ccos%28a%29%5Ccos%28b%29%2B%5Csin%28a%29%5Csin%28b%29)
![\tan(a-b)=\frac{\tan(a)-\tan(b)}{1+\tan(a)\tan(b)}](https://tex.z-dn.net/?f=%5Ctan%28a-b%29%3D%5Cfrac%7B%5Ctan%28a%29-%5Ctan%28b%29%7D%7B1%2B%5Ctan%28a%29%5Ctan%28b%29%7D)
Let's apply the difference identities to all three terms:
![-[\sin(-t)\cos(8\pi)+\cos(-t)\sin(8\pi)]+[\cos(-t)\cos(2\pi)+\sin(-t)\sin(2\pi)]+\frac{\tan(-t)-\tan(5\pi)}{1+\tan(-t)\tan(5\pi)}](https://tex.z-dn.net/?f=-%5B%5Csin%28-t%29%5Ccos%288%5Cpi%29%2B%5Ccos%28-t%29%5Csin%288%5Cpi%29%5D%2B%5B%5Ccos%28-t%29%5Ccos%282%5Cpi%29%2B%5Csin%28-t%29%5Csin%282%5Cpi%29%5D%2B%5Cfrac%7B%5Ctan%28-t%29-%5Ctan%285%5Cpi%29%7D%7B1%2B%5Ctan%28-t%29%5Ctan%285%5Cpi%29%7D)
We are about to use that cos(even*pi) is 1 and sin(even*pi) is 0 so tan(odd*pi)=0:
![-[\sin(-t)(1)+\cos(-t)(0)]+[\cos(-t)(1)+\sin(-t)(0)]+\frac{\tan(-t)-0}{1+\tan(-t)(0)](https://tex.z-dn.net/?f=-%5B%5Csin%28-t%29%281%29%2B%5Ccos%28-t%29%280%29%5D%2B%5B%5Ccos%28-t%29%281%29%2B%5Csin%28-t%29%280%29%5D%2B%5Cfrac%7B%5Ctan%28-t%29-0%7D%7B1%2B%5Ctan%28-t%29%280%29)
Cleaning up the algebra:
![-[\sin(-t)]+[\cos(-t)]+\frac{\tan(-t)}{1}](https://tex.z-dn.net/?f=-%5B%5Csin%28-t%29%5D%2B%5B%5Ccos%28-t%29%5D%2B%5Cfrac%7B%5Ctan%28-t%29%7D%7B1%7D)
Cleaning up more algebra:
![-\sin(-t)+\cos(-t)+\tan(-t)](https://tex.z-dn.net/?f=-%5Csin%28-t%29%2B%5Ccos%28-t%29%2B%5Ctan%28-t%29)
Applying that sine and tangent is odd while cosine is even. That is,
sin(-x)=-sin(x) and tan(-x)=-tan(x) while cos(-x)=cos(x):
![\sin(t)+\cos(t)-\tan(t)](https://tex.z-dn.net/?f=%5Csin%28t%29%2B%5Ccos%28t%29-%5Ctan%28t%29)
Making the substitution the problem wanted us to:
![a+b-c](https://tex.z-dn.net/?f=a%2Bb-c)
Just for fun you could have wrote c as a/b too since tangent=sine/cosine.
50 feet by 13 feet is 650 square foot. They can only afford a 180 square foot banner. Yes it can fit but it would be smaller by 470 feet.
Answer:
5.507605086
5.50
Step-by-step explanation:
-> 40 hours per week, 52 weeks a year
<u>shop and save grocers</u>
monthly wages: $3,800
hourly wages: $3800 / 160 = $23.75 per hour
yearly wages: $23.75 per hour x 40 hours per week x 52 weeks a year
= $49,400
<u>unbelievable toys</u>
yearly wages: $43,000
<u>convenience store</u>
$16.50 per hour x 40 hours per week x 52 weeks a year
= $34,320
49,400 - 34,320 = 15,080
..? that's not even an answer choice what-