![\sin(x-y)=\sin x\cos y-\sin y\cos x](https://tex.z-dn.net/?f=%5Csin%28x-y%29%3D%5Csin%20x%5Ccos%20y-%5Csin%20y%5Ccos%20x)
Since
![\cos x=\dfrac8{17}](https://tex.z-dn.net/?f=%5Ccos%20x%3D%5Cdfrac8%7B17%7D)
, you have
![\sin x=\sqrt{1-\cos^2x}=\sqrt{1-\left(\dfrac8{17}\right)^2}=\dfrac{15}{17}](https://tex.z-dn.net/?f=%5Csin%20x%3D%5Csqrt%7B1-%5Ccos%5E2x%7D%3D%5Csqrt%7B1-%5Cleft%28%5Cdfrac8%7B17%7D%5Cright%29%5E2%7D%3D%5Cdfrac%7B15%7D%7B17%7D)
and since
![\cos y=\dfrac35](https://tex.z-dn.net/?f=%5Ccos%20y%3D%5Cdfrac35)
, you have
![\sin y=\sqrt{1-\cos^2y}=\sqrt{1-\left(\dfrac35\right)^2}=\dfrac45](https://tex.z-dn.net/?f=%5Csin%20y%3D%5Csqrt%7B1-%5Ccos%5E2y%7D%3D%5Csqrt%7B1-%5Cleft%28%5Cdfrac35%5Cright%29%5E2%7D%3D%5Cdfrac45)
So,
![\sin(x-y)=\dfrac{15}{17}\times\dfrac35-\dfrac45\times\dfrac8{17}=\dfrac{13}{85}](https://tex.z-dn.net/?f=%5Csin%28x-y%29%3D%5Cdfrac%7B15%7D%7B17%7D%5Ctimes%5Cdfrac35-%5Cdfrac45%5Ctimes%5Cdfrac8%7B17%7D%3D%5Cdfrac%7B13%7D%7B85%7D)
Note that this assumes that both
![\sin x](https://tex.z-dn.net/?f=%5Csin%20x)
and
![\sin y](https://tex.z-dn.net/?f=%5Csin%20y)
are positive, or
![0](https://tex.z-dn.net/?f=0%3Cx%3C%5Cpi)
.
Positive whole numbers less than 13 are
1,2,3,4,5,6,7,8,9,10,11,12
less than means not including
Answer:
1/6
Step-by-step explanation:
Make the denominators the same by finding the lcm(least common denominator). The least common demominator would be 24. So multiply both numbers in 1/8 by 3. This would eaqual 3/24. Multiply both numbersin 4/3 by 8. This would equal
=
. Simplify 96/576 by dividing both numbers by 96.
<u>96</u> ÷ 96 = <u> 1 </u> 576 ÷ 96 = 6 and that becomes 1/6.