we can factor the whole thing:
(2sin(x) -1)(sin(x)+1) = 0.
Therefore, sin(x) = -1 and sin(x) = 1/2.
For the first one x = 3π/2 and the second is π/6 and 5π/6
So 3π/2, π/6 and 5π/6 are the solutions.
I do kind of have a problem with this because it doesn't mention if you should go over 360°. Otherwise, you have to add in an 2nπ into the equations like 3π/2 + 2nπ; ![n \in \mathbb{W}](https://tex.z-dn.net/?f=n%20%5Cin%20%5Cmathbb%7BW%7D)
but I don't know if that is necessary for you.
<span>89 is the correct answer.
</span>
A
Step-by-step explanation:
90 Degree Rotation. When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). ...
180 Degree Rotation. When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). ...
270 Degree Rotation.
Answer:
![x=\frac{1}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%7D%7B4%7D)
Step-by-step explanation:
<u>Given:</u>
![2log(\frac{2}{3})=\frac{1}{2}log(x)-log(18)+log(16)](https://tex.z-dn.net/?f=2log%28%5Cfrac%7B2%7D%7B3%7D%29%3D%5Cfrac%7B1%7D%7B2%7Dlog%28x%29-log%2818%29%2Blog%2816%29)
<u>Use the Power Rule Law:</u>
![log(\frac{2}{3}^2)=log(x^{1/2})+log(16)-log(18)](https://tex.z-dn.net/?f=log%28%5Cfrac%7B2%7D%7B3%7D%5E2%29%3Dlog%28x%5E%7B1%2F2%7D%29%2Blog%2816%29-log%2818%29)
<u>Use the Quotient Rule Law:</u>
![log(\frac{4}{9})=log(\sqrt{x})+log(\frac{16}{18})](https://tex.z-dn.net/?f=log%28%5Cfrac%7B4%7D%7B9%7D%29%3Dlog%28%5Csqrt%7Bx%7D%29%2Blog%28%5Cfrac%7B16%7D%7B18%7D%29)
<u>Use the Product Rule Law:</u>
![log(\frac{4}{9})=log(\frac{16\sqrt{x}}{18})](https://tex.z-dn.net/?f=log%28%5Cfrac%7B4%7D%7B9%7D%29%3Dlog%28%5Cfrac%7B16%5Csqrt%7Bx%7D%7D%7B18%7D%29)
<u>Simplify:</u>
![log(\frac{4}{9})=log(\frac{8\sqrt{x}}{9})](https://tex.z-dn.net/?f=log%28%5Cfrac%7B4%7D%7B9%7D%29%3Dlog%28%5Cfrac%7B8%5Csqrt%7Bx%7D%7D%7B9%7D%29)
![\frac{4}{9}=\frac{8\sqrt{x}}{9}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B9%7D%3D%5Cfrac%7B8%5Csqrt%7Bx%7D%7D%7B9%7D)
![4=8\sqrt{x}](https://tex.z-dn.net/?f=4%3D8%5Csqrt%7Bx%7D)
![\frac{4}{8}=\sqrt{x}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B8%7D%3D%5Csqrt%7Bx%7D)
![\frac{1}{2}=\sqrt{x}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%3D%5Csqrt%7Bx%7D)
![\frac{1}{4}=x](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%3Dx)