Answer:
![cot x = \frac{cos x}{sin x}](https://tex.z-dn.net/?f=%20cot%20x%20%3D%20%5Cfrac%7Bcos%20x%7D%7Bsin%20x%7D)
![cos x \frac{cos x}{sin x} + sin x](https://tex.z-dn.net/?f=%20cos%20x%20%5Cfrac%7Bcos%20x%7D%7Bsin%20x%7D%20%2B%20sin%20x)
![\frac{cos^2 x}{sin x} +sin x](https://tex.z-dn.net/?f=%20%5Cfrac%7Bcos%5E2%20x%7D%7Bsin%20x%7D%20%2Bsin%20x)
![sin^2 x + cos^2 x =1](https://tex.z-dn.net/?f=%20sin%5E2%20x%20%2B%20cos%5E2%20x%20%3D1%20)
Solving for
we got
and replacing this we got:
![\frac{1-sin^2 x}{sin x} +sin x](https://tex.z-dn.net/?f=%20%5Cfrac%7B1-sin%5E2%20x%7D%7Bsin%20x%7D%20%2Bsin%20x%20)
![\frac{1}{sin x} -\frac{sin^2 x}{sin x} +sin x](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7Bsin%20x%7D%20-%5Cfrac%7Bsin%5E2%20x%7D%7Bsin%20x%7D%20%2Bsin%20x)
![csc x -sin x + sin x = csc x](https://tex.z-dn.net/?f=%20csc%20x%20-sin%20x%20%2B%20sin%20x%20%3D%20csc%20x)
And then the best option for this case would be:
b.csc x
Step-by-step explanation:
For this case we have the following expression given:
![cos x cot x + sin x](https://tex.z-dn.net/?f=%20cos%20x%20cot%20x%20%2B%20sin%20x%20)
We know from math properties that the definition for cot is ![cot x = \frac{cos x}{sin x}](https://tex.z-dn.net/?f=%20cot%20x%20%3D%20%5Cfrac%7Bcos%20x%7D%7Bsin%20x%7D)
If we use this definition we got:
![cos x \frac{cos x}{sin x} + sin x](https://tex.z-dn.net/?f=%20cos%20x%20%5Cfrac%7Bcos%20x%7D%7Bsin%20x%7D%20%2B%20sin%20x)
![\frac{cos^2 x}{sin x} +sin x](https://tex.z-dn.net/?f=%20%5Cfrac%7Bcos%5E2%20x%7D%7Bsin%20x%7D%20%2Bsin%20x)
Now we can use the following identity:
![sin^2 x + cos^2 x =1](https://tex.z-dn.net/?f=%20sin%5E2%20x%20%2B%20cos%5E2%20x%20%3D1%20)
Solving for
we got
and replacing this we got:
![\frac{1-sin^2 x}{sin x} +sin x](https://tex.z-dn.net/?f=%20%5Cfrac%7B1-sin%5E2%20x%7D%7Bsin%20x%7D%20%2Bsin%20x%20)
![\frac{1}{sin x} -\frac{sin^2 x}{sin x} +sin x](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7Bsin%20x%7D%20-%5Cfrac%7Bsin%5E2%20x%7D%7Bsin%20x%7D%20%2Bsin%20x)
![csc x -sin x + sin x = csc x](https://tex.z-dn.net/?f=%20csc%20x%20-sin%20x%20%2B%20sin%20x%20%3D%20csc%20x)
And then the best option for this case would be:
b.csc x
Answer:
The zeros are x=0,x=8
Step-by-step explanation:
f(x)=x(x-8)
To find the zeros, we set the equation equal to zero
0 = x(x-8)
Using the zero product property
x= 0 x-8=0
x=0 x=8
The zeros are 0,8
Answer:
Slope: 0
Step-by-step explanation:
(-3,5) (4,5)
y2-y1/x2-x1
5-5/4+3=0/7
0/7 simplifies to 0.
So the slope of the line (-3,5) (4,5) is 0.
Hope this helps! ;)
Answer:
64 degrees
Step-by-step explanation:
Lets find the measure of the other angle in the other triangle with measures of 84 and 36.
Since there are 180 degrees in a triangle, we just add the other two angles and subtract from 180:
84 + 36 = 120
180 - 120 = 60
So the measure of the other angle in the other triangle is 60. Since there is a right angle we subtract 60 from 90
90 - 60 = 30
So the triangle with the missing angle has two angles with measures of 86 and 30. Now we add the measures and subtract from 180 again.
86 + 30 = 116
180 - 116 = 64
So the missing angle has a measure of 64 degrees