We have to prove that the tangent is an odd function.
If the tangent is an odd function, the following condition should be satisfied:
![\tan(t)=-\tan(-t)](https://tex.z-dn.net/?f=%5Ctan%28t%29%3D-%5Ctan%28-t%29)
From the figure we can see that the tangent can be expressed as:
We can start then from tan(t) and will try to arrive to -tan(-t):
![\begin{gathered} \tan(t)=\frac{\sin(t)}{cos(t)}=\frac{y}{x} \\ \tan(t)=\frac{-(-y)}{x}=\frac{-\sin(-t)}{\cos(-t)} \\ \tan(t)=-\frac{\sin(-t)}{\cos(-t)} \\ \tan(t)=-\tan(-t) \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctan%28t%29%3D%5Cfrac%7B%5Csin%28t%29%7D%7Bcos%28t%29%7D%3D%5Cfrac%7By%7D%7Bx%7D%20%5C%5C%20%5Ctan%28t%29%3D%5Cfrac%7B-%28-y%29%7D%7Bx%7D%3D%5Cfrac%7B-%5Csin%28-t%29%7D%7B%5Ccos%28-t%29%7D%20%5C%5C%20%5Ctan%28t%29%3D-%5Cfrac%7B%5Csin%28-t%29%7D%7B%5Ccos%28-t%29%7D%20%5C%5C%20%5Ctan%28t%29%3D-%5Ctan%28-t%29%20%5Cend%7Bgathered%7D)
We have arrived to the condition for odd functions, so we have just proved that the tangent function is an odd function.
Ya have to round it to the nearest hundred, so that would be 2 thousand.
so it's 4,552,000
Answer:
1.76
Step-by-step explanation:
Answer:
the domain in general is negative Infinity, infinity.
Step-by-step explanation:
Infinity means it is a straight line that goes on forever it never stops. graph the -6 and 1. I am not totally sure what domain restrictions are if you have an equation for it go a head and put it there and I can help you more.
Answer:
So this means the bus B covered 390-120=270 miles when bus A has already reached 390 miles.
270 miles
Step-by-step explanation:
So is A is going faster than B so A will reach the destination first.
When will A reach it's destination?
Let's find out.
To solve this problem, the following will come in handy:
Speed=distance/time or time*Speed=distance or time=distance/speed .
time=distance/speed
![T_A=\frac{390}{S_A}](https://tex.z-dn.net/?f=T_A%3D%5Cfrac%7B390%7D%7BS_A%7D)
![T_A=\frac{390}{65}](https://tex.z-dn.net/?f=T_A%3D%5Cfrac%7B390%7D%7B65%7D)
![T_A=6](https://tex.z-dn.net/?f=T_A%3D6)
So it will take bus A 6 hours to cover the distance of 390 miles.
How much time would have it taken bus B to reach that same distance?
![T_B=\frac{390}{45}](https://tex.z-dn.net/?f=T_B%3D%5Cfrac%7B390%7D%7B45%7D)
![T_B=8.\overline{6}](https://tex.z-dn.net/?f=T_B%3D8.%5Coverline%7B6%7D)
So it would have taken bus B
hours to cover a distance of 390 miles.
So the time difference is
hours.
It will take
more hours than bus A for bus B to complete a distance of 390 miles.
So bus B traveled
miles (used the time*speed=distance) after bus A got to it's destination.
So this means the bus B covered 390-120=270 miles when bus A has already reached 390 miles.