Answer:
angle 3= 53
angle2= 53
angle 4 =
Step-by-step explanation:
<span>|x| is x if x>0
|x| is -x if x<0
|x| is 0 if x=0
so
(|x|)'=1 when x>0
so
(|x|)'=-1 when x<0
</span><span> (|2x-4|)'=2 when x>2
and
(|2x-4|)'=-2 when x<2
</span>
<span>Therefore the left derivative doesn't equal the right derivative as x approaches 2.</span>
Take a common factor of cos(x)
![\cos(x) (1 + 2 \sin(x) ) = 0](https://tex.z-dn.net/?f=%20%5Ccos%28x%29%20%281%20%2B%202%20%5Csin%28x%29%20%29%20%3D%200)
then by zero multplication rules
![\cos(x) = 0](https://tex.z-dn.net/?f=%20%5Ccos%28x%29%20%20%3D%200)
![x = \frac{\pi}{2} \: x = \frac{3\pi}{2}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B%5Cpi%7D%7B2%7D%20%20%5C%3A%20x%20%3D%20%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%20)
and when
![1 + 2 \sin(x) = 0](https://tex.z-dn.net/?f=1%20%2B%202%20%5Csin%28x%29%20%20%3D%200)
so
![2 \sin(x ) = - 1](https://tex.z-dn.net/?f=2%20%5Csin%28x%20%29%20%3D%20%20-%201)
![\sin(x) = \frac{ - 1}{2}](https://tex.z-dn.net/?f=%20%5Csin%28x%29%20%20%3D%20%20%5Cfrac%7B%20-%201%7D%7B2%7D%20)
so
![x = \frac{3\pi}{2} - \frac{\pi}{3}](https://tex.z-dn.net/?f=x%20%3D%20%20%20%5Cfrac%7B3%5Cpi%7D%7B2%7D%20%20-%20%20%5Cfrac%7B%5Cpi%7D%7B3%7D%20)
and