If you need to figure out X it would be 60
Answer:
4
Step-by-step explanation:
![\tan a=-\dfrac{12}5](https://tex.z-dn.net/?f=%5Ctan%20a%3D-%5Cdfrac%7B12%7D5)
Recall the following identities:
![1+\tan^2a=\sec^2a=\dfrac1{\cos^2a}](https://tex.z-dn.net/?f=1%2B%5Ctan%5E2a%3D%5Csec%5E2a%3D%5Cdfrac1%7B%5Ccos%5E2a%7D)
![\cos^2a=\dfrac{1+\cos2a}a](https://tex.z-dn.net/?f=%5Ccos%5E2a%3D%5Cdfrac%7B1%2B%5Ccos2a%7Da)
from which we get
![1+\left(-\dfrac{12}5\right)^2=\dfrac1{\cos^2a}](https://tex.z-dn.net/?f=1%2B%5Cleft%28-%5Cdfrac%7B12%7D5%5Cright%29%5E2%3D%5Cdfrac1%7B%5Ccos%5E2a%7D)
![\implies\cos^2a=\dfrac{25}{169}](https://tex.z-dn.net/?f=%5Cimplies%5Ccos%5E2a%3D%5Cdfrac%7B25%7D%7B169%7D)
Since
![a](https://tex.z-dn.net/?f=a)
is in the fourth quadrant
![\left(\dfrac{3\pi}2](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7B3%5Cpi%7D2%3Ca%3C2%5Cpi%5Cright%29)
we know that
![\cos a](https://tex.z-dn.net/?f=%5Ccos%20a)
should be positive, so when we take the square root here, we should take the positive root.
![\implies\cos a=\sqrt{\dfrac{25}{169}}=\dfrac5{13}](https://tex.z-dn.net/?f=%5Cimplies%5Ccos%20a%3D%5Csqrt%7B%5Cdfrac%7B25%7D%7B169%7D%7D%3D%5Cdfrac5%7B13%7D)
Now recall that
![\cos^2a+\sin^2a=1](https://tex.z-dn.net/?f=%5Ccos%5E2a%2B%5Csin%5E2a%3D1)
and since
![a](https://tex.z-dn.net/?f=a)
is in the fourth quadrant, we expect
![\sin a](https://tex.z-dn.net/?f=%5Csin%20a)
to be negative. So,
![\sin^2a=1-\cos^2a=\dfrac{144}{169}\implies\sin a=-\sqrt{\dfrac{144}{169}}=-\dfrac{12}{13}](https://tex.z-dn.net/?f=%5Csin%5E2a%3D1-%5Ccos%5E2a%3D%5Cdfrac%7B144%7D%7B169%7D%5Cimplies%5Csin%20a%3D-%5Csqrt%7B%5Cdfrac%7B144%7D%7B169%7D%7D%3D-%5Cdfrac%7B12%7D%7B13%7D)
One final identity:
![\sin2a=2\sin a\cos a](https://tex.z-dn.net/?f=%5Csin2a%3D2%5Csin%20a%5Ccos%20a)
from which we get
Answer:
Dependent
Step-by-step explanation:
Because there is only one function to the equation.
Answer:
160 months
Step-by-step explanation:
just took that ap3x quiz yerrr