Answer:
![\theta \in \{0,\pi,\frac{7\pi}{6},\frac{11\pi}{6}\}](https://tex.z-dn.net/?f=%5Ctheta%20%5Cin%20%5C%7B0%2C%5Cpi%2C%5Cfrac%7B7%5Cpi%7D%7B6%7D%2C%5Cfrac%7B11%5Cpi%7D%7B6%7D%5C%7D)
Step-by-step explanation:
![\sin(\theta)+1=\cos(2\theta)](https://tex.z-dn.net/?f=%5Csin%28%5Ctheta%29%2B1%3D%5Ccos%282%5Ctheta%29)
Applying double angle identity:
![\cos(2\theta)=1-2\sin^2(\theta)](https://tex.z-dn.net/?f=%5Ccos%282%5Ctheta%29%3D1-2%5Csin%5E2%28%5Ctheta%29)
Doing so would give:
![\sin(\theta)+1=1-2\sin^2(\theta)](https://tex.z-dn.net/?f=%5Csin%28%5Ctheta%29%2B1%3D1-2%5Csin%5E2%28%5Ctheta%29)
We need to get everything to one side so we have 0 on one side.
Subtract 1 on both sides:
![\sin(\theta)=-2\sin^2(\theta)](https://tex.z-dn.net/?f=%5Csin%28%5Ctheta%29%3D-2%5Csin%5E2%28%5Ctheta%29)
Add
on both sides:
![\sin(\theta)+2\sin^2(\theta)=0](https://tex.z-dn.net/?f=%5Csin%28%5Ctheta%29%2B2%5Csin%5E2%28%5Ctheta%29%3D0)
Let's factor the left-hand side.
The two terms on the left-hand side have a common factor of
.
.
This implies we have:
.
We need to solve both equations.
You are asking they be solved in the interval
.
![\sin(\theta)=0](https://tex.z-dn.net/?f=%5Csin%28%5Ctheta%29%3D0)
This means look at your unit circle and find when you have your y-coordinates is 0.
You this at 0 and
. (I didn't include
because you don't have a equal sign at the endpoint of
.
Now let's solve ![1+2\sin(\theta)=0](https://tex.z-dn.net/?f=1%2B2%5Csin%28%5Ctheta%29%3D0)
Subtract 1 on both sides:
![2\sin(\theta)=-1](https://tex.z-dn.net/?f=2%5Csin%28%5Ctheta%29%3D-1)
Divide both sides by 2:
![\sin(\theta)=\frac{-1}{2}](https://tex.z-dn.net/?f=%5Csin%28%5Ctheta%29%3D%5Cfrac%7B-1%7D%7B2%7D)
Now we are going to go and look for when the y-coordinates are -1/2.
This happens at
and
.
The solution set given the restrictions is
![\theta \in \{0,\pi,\frac{7\pi}{6},\frac{11\pi}{6}\}](https://tex.z-dn.net/?f=%5Ctheta%20%5Cin%20%5C%7B0%2C%5Cpi%2C%5Cfrac%7B7%5Cpi%7D%7B6%7D%2C%5Cfrac%7B11%5Cpi%7D%7B6%7D%5C%7D)
Answer:
they are both going in the same dirrection but this does not mean they are parrallel or perpendicular.
Step-by-step explanation:
So just say neither
Answer:
2√15
Step-by-step explanation:
The division is: 2x³+2x+4
<h3>What is synthetic division?</h3>
Synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division.
Given:
(2
+ 4x³ + 2x² + 8x + 8) ÷ (x + 2)
The division is attached below.
Hence, the division is 2x³+2x+4.
Learn more about this concept here:
brainly.com/question/3696665
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