Not sure why such an old question is showing up on my feed...
Anyway, let
![x=\tan^{-1}\dfrac43](https://tex.z-dn.net/?f=x%3D%5Ctan%5E%7B-1%7D%5Cdfrac43)
and
![y=\sin^{-1}\dfrac35](https://tex.z-dn.net/?f=y%3D%5Csin%5E%7B-1%7D%5Cdfrac35)
. Then we want to find the exact value of
![\cos(x-y)](https://tex.z-dn.net/?f=%5Ccos%28x-y%29)
.
Use the angle difference identity:
![\cos(x-y)=\cos x\cos y+\sin x\sin y](https://tex.z-dn.net/?f=%5Ccos%28x-y%29%3D%5Ccos%20x%5Ccos%20y%2B%5Csin%20x%5Csin%20y)
and right away we find
![\sin y=\dfrac35](https://tex.z-dn.net/?f=%5Csin%20y%3D%5Cdfrac35)
. By the Pythagorean theorem, we also find
![\cos y=\dfrac45](https://tex.z-dn.net/?f=%5Ccos%20y%3D%5Cdfrac45)
. (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)
Meanwhile, if
![\tan x=\dfrac43](https://tex.z-dn.net/?f=%5Ctan%20x%3D%5Cdfrac43)
, then (by Pythagorean theorem)
![\sec x=\dfrac53](https://tex.z-dn.net/?f=%5Csec%20x%3D%5Cdfrac53)
, so
![\cos x=\dfrac35](https://tex.z-dn.net/?f=%5Ccos%20x%3D%5Cdfrac35)
. And from this,
![\sin x=\dfrac45](https://tex.z-dn.net/?f=%5Csin%20x%3D%5Cdfrac45)
.
So,
Answer:
hope it will help you
Step-by-step explanation:
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Answer:
51.6666666667
Step-by-step explanation:
Answer:
The probability is
or 25%
Step-by-step explanation:
The question states the total number of vehicles, as well as the number of damaged vehicles on a yearly basis. If 50 vehicles in every 200 vehicles per year are damaged, then we can obtain:
Probability of a damaged vehicle in any given year = ![\frac{Number of Damaged Vehicles}{Total Number of Vehicles}](https://tex.z-dn.net/?f=%5Cfrac%7BNumber%20of%20Damaged%20Vehicles%7D%7BTotal%20Number%20of%20Vehicles%7D)
=
=
or 25%