Starting from the fundamental trigonometric equation, we have
![\cos^2(\alpha)+\sin^2(\alpha)=1 \iff \sin(\alpha)=\pm\sqrt{1-\cos^2(\alpha)}](https://tex.z-dn.net/?f=%5Ccos%5E2%28%5Calpha%29%2B%5Csin%5E2%28%5Calpha%29%3D1%20%5Ciff%20%5Csin%28%5Calpha%29%3D%5Cpm%5Csqrt%7B1-%5Ccos%5E2%28%5Calpha%29%7D)
Since
, we know that the angle lies in the third quadrant, where both sine and cosine are negative. So, in this specific case, we have
![\sin(\alpha)=-\sqrt{1-\cos^2(\alpha)}](https://tex.z-dn.net/?f=%5Csin%28%5Calpha%29%3D-%5Csqrt%7B1-%5Ccos%5E2%28%5Calpha%29%7D)
Plugging the numbers, we have
![\sin(\alpha)=-\sqrt{1-\dfrac{64}{289}}=-\sqrt{\dfrac{225}{289}}=-\dfrac{15}{17}](https://tex.z-dn.net/?f=%5Csin%28%5Calpha%29%3D-%5Csqrt%7B1-%5Cdfrac%7B64%7D%7B289%7D%7D%3D-%5Csqrt%7B%5Cdfrac%7B225%7D%7B289%7D%7D%3D-%5Cdfrac%7B15%7D%7B17%7D)
Now, just recall that
![\sin(-\alpha)=-\sin(\alpha)](https://tex.z-dn.net/?f=%5Csin%28-%5Calpha%29%3D-%5Csin%28%5Calpha%29)
to deduce
![\sin(-\alpha)=-\sin(\alpha)=-\left(-\dfrac{15}{17}\right)=\dfrac{15}{17}](https://tex.z-dn.net/?f=%5Csin%28-%5Calpha%29%3D-%5Csin%28%5Calpha%29%3D-%5Cleft%28-%5Cdfrac%7B15%7D%7B17%7D%5Cright%29%3D%5Cdfrac%7B15%7D%7B17%7D)
Answer:
x=1
Step-by-step explanation:
6-3x=5x-10x+8=
move all terms to the left:
6-3x-(5x-10x+8)=0
add all the numbers together, and all the variables
-3x-(-5x+8)+6=0
get rid of parentheses
-3x+5x-8+6=0
add all the numbers together, and all the variables
2x-2=0
move all terms containing x to the left, all other terms to the right
2x=2
x=2/2
x=1
Answer:
The soda costs 2.20 and the sandwich costs 7.70
Step-by-step explanation:
To find this, set the soda cost as x. We now know that the sandwich cost is 3.5x. Add these together and set equal to 9.90
x + 3.5x = 9.90
4.5x = 9.90
x = 2.20
This is the cost of the soda. Now we can multiply that by 3.5 to get the sandwich cost.
3.5 * 2.20 = 7.70
Answer:
y= $25-$10.50
Step-by-step explanation:
Answer: 15
Step-by-step explanation:
360 is the amount of sweats you need to ship to a costumer. One box has 24 shirts. This gives you the equation: 360 ÷ 24 = 15.
N is 15