Answer:
(x,y)= (-92/35,233/70)
Step-by-step explanation:
Recall the Pythagorean identity,
![\sin^2(x) + \cos^2(x) = 1](https://tex.z-dn.net/?f=%5Csin%5E2%28x%29%20%2B%20%5Ccos%5E2%28x%29%20%3D%201)
Then we can rewrite the equation as
![\sin(3x) + 2 \cos^2(3x) = 1](https://tex.z-dn.net/?f=%5Csin%283x%29%20%2B%202%20%5Ccos%5E2%283x%29%20%3D%201)
![\sin(3x) + 2 (1 - \sin^2(3x)) = 1](https://tex.z-dn.net/?f=%5Csin%283x%29%20%2B%202%20%281%20-%20%5Csin%5E2%283x%29%29%20%3D%201)
![1 + \sin(3x) - 2 \sin^2(3x) = 0](https://tex.z-dn.net/?f=1%20%2B%20%5Csin%283x%29%20-%202%20%5Csin%5E2%283x%29%20%3D%200)
Factorize the left side.
![(1 + 2 \sin(3x)) (1 - \sin(3x)) = 0](https://tex.z-dn.net/?f=%281%20%2B%202%20%5Csin%283x%29%29%20%281%20-%20%5Csin%283x%29%29%20%3D%200)
Then we have
![1 + 2\sin(3x) = 0 \text{ or } 1 - \sin(3x) = 0](https://tex.z-dn.net/?f=1%20%2B%202%5Csin%283x%29%20%3D%200%20%5Ctext%7B%20or%20%7D%201%20-%20%5Csin%283x%29%20%3D%200)
![\sin(3x) = -\dfrac12 \text{ or } \sin(3x) = 1](https://tex.z-dn.net/?f=%5Csin%283x%29%20%3D%20-%5Cdfrac12%20%5Ctext%7B%20or%20%7D%20%5Csin%283x%29%20%3D%201)
Solve for
. We get two families of solutions:
![3x = \sin^{-1}\left(-\dfrac12\right) + 2n\pi \text{ or } 3x = \pi - \sin^{-1}\left(-\dfrac12\right) + 2n\pi](https://tex.z-dn.net/?f=3x%20%3D%20%5Csin%5E%7B-1%7D%5Cleft%28-%5Cdfrac12%5Cright%29%20%2B%202n%5Cpi%20%5Ctext%7B%20or%20%7D%203x%20%3D%20%5Cpi%20-%20%5Csin%5E%7B-1%7D%5Cleft%28-%5Cdfrac12%5Cright%29%20%2B%202n%5Cpi)
![\implies 3x = -\dfrac\pi6 + 2n\pi \text{ or } 3x = \dfrac{7\pi}6 + 2n\pi](https://tex.z-dn.net/?f=%5Cimplies%203x%20%3D%20-%5Cdfrac%5Cpi6%20%2B%202n%5Cpi%20%5Ctext%7B%20or%20%7D%203x%20%3D%20%5Cdfrac%7B7%5Cpi%7D6%20%2B%202n%5Cpi)
![\implies \boxed{x = -\dfrac\pi{18} + \dfrac{2n\pi}3} \text{ or } \boxed{x = \dfrac{7\pi}{18} + \dfrac{2n\pi}3}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cboxed%7Bx%20%3D%20-%5Cdfrac%5Cpi%7B18%7D%20%2B%20%5Cdfrac%7B2n%5Cpi%7D3%7D%20%5Ctext%7B%20or%20%7D%20%5Cboxed%7Bx%20%3D%20%5Cdfrac%7B7%5Cpi%7D%7B18%7D%20%2B%20%5Cdfrac%7B2n%5Cpi%7D3%7D)
and
![3x = \sin^{-1}(1) + 2n\pi](https://tex.z-dn.net/?f=3x%20%3D%20%5Csin%5E%7B-1%7D%281%29%20%2B%202n%5Cpi)
![\implies 3x = \dfrac\pi2 + 2n\pi](https://tex.z-dn.net/?f=%5Cimplies%203x%20%3D%20%5Cdfrac%5Cpi2%20%2B%202n%5Cpi)
![\implies \boxed{x = \dfrac\pi6 + \dfrac{2n\pi}3}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cboxed%7Bx%20%3D%20%5Cdfrac%5Cpi6%20%2B%20%5Cdfrac%7B2n%5Cpi%7D3%7D)
(where
is any integer)
Answer:
about 80º give or take
Step-by-step explanation:
it's not quite 90 degrees, and its not 70 degrees or below.
Answer:
The value of the given expression when z=27 is 16
Therefore
when z=27
Step-by-step explanation:
Given expression is ![\frac{7}{9}(z-18)+\frac{1}{3}z](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B9%7D%28z-18%29%2B%5Cfrac%7B1%7D%7B3%7Dz)
To find the value of the expression when z=27 :
First simplify the given expression
![\frac{7}{9}(z-18)+\frac{1}{3}z](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B9%7D%28z-18%29%2B%5Cfrac%7B1%7D%7B3%7Dz)
![=\frac{7(z-18)}{9}+\frac{1}{3}z](https://tex.z-dn.net/?f=%3D%5Cfrac%7B7%28z-18%29%7D%7B9%7D%2B%5Cfrac%7B1%7D%7B3%7Dz)
![=\frac{7z-126}{9}+\frac{1}{3}z](https://tex.z-dn.net/?f=%3D%5Cfrac%7B7z-126%7D%7B9%7D%2B%5Cfrac%7B1%7D%7B3%7Dz)
![=\frac{7z-126+3z}{9}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B7z-126%2B3z%7D%7B9%7D)
Put z=27 in the above equation we get
![=\frac{144}{9}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B144%7D%7B9%7D)
![=\frac{144}{9}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B144%7D%7B9%7D)
![=16](https://tex.z-dn.net/?f=%3D16)
Therefore the value of the given expression when z=27 is 16
Therefore
when z=27
Answer:
C
Step-by-step explanation: