Answer:
sqrt(2)/2
Step-by-step explanation:
Given tan(x)=2-cot(x), find sin(x).
Rewrite in terms of sine and cosine:
sin(x)/cos(x)=2-cos(x)/sin(x)
Multiply both sides by cos(x)sin(x):
sin^2(x)=2sin(x)cos(x)-cos^2(x)
Rewrite cos^2(x) using the identity sin^2(x)+cos^2(x)=1:
sin^2(x)=2sin(x)cos(x)-(1-sin^2(x))
Distribute:
sin^2(x)=2sin(x)cos(x)-1+sin^2(x)
Subtracting sin^2(x) on both sides:
0=2sin(x)cos(x)-1
Add 1 on both sides:
1=2sin(x)cos(x)
Use identity sin(2x)=2sin(x)cos(x) to rewrite right:
1=sin(2x)
Since sin(pi/2)=1, then 2x=pi/2.
Dividing both sides by 2 gives x=pi/4.
So sin(pi/4)=sqrt(2)/2
Answer:
$3.90
Step-by-step explanation:
Are you asking how much cases is needed to to reach the 90 units? If yes then 90/8 which would give you 11.25. But since it’s by case then round up to get 12 cases. I think I answered it wrong but
Looking through the table, the rainfall (in inches) goes down by 00.53 inches.
Therefore, you could say that,
"The average rate of change is 00.53. This means that each year the amount of rainfall in inches goes down by 00.53."
Answer:
4
Step-by-step explanation:
The diagram shows that the one triangle can be divided into two equal right triangles. Because of this, you can use the Pythagorean Theorem to solve this problem. a and b are the two sides of the angles, and c is the hypotenuse.
The given lengths are 5 as the hypotenuse and 3 as one length. (You have 3 as a given length because the two triangles have a length of 6 on one side. 6/2 = 3)
a² + b² = c²
a² = c² - b²
a² = 5² - 3²
a² = 25² - 9²
a² = 16
a = 4
