If x is in quadrant I, then both sin(x) and cos(x) are positive. The angle x/2 also belongs to quadrant I, and hence each of sin(x/2), cos(x/2), and tan(x/2) are positive.
Recall that for all x,
cos²(x) + sin²(x) = 1
and multiplying through both sides by 1/cos²(x) = sec²(x) gives another flavor of this identity,
1 + tan²(x) = sec²(x)
It follows that
sec(x) = √(1 + tan²(x)) = √937/19
which immediately gives us
cos(x) = 19/√937
and from the identity above we find
sin(x) = √(1 - cos²(x)) = 24/√937
Recall the half angle identity for cos :
cos²(x) = (1 + cos(2x))/2
which means
cos(x/2) = + √[(1 + cos(x))/2] = √[1/2 + 19/(2√937)]
Then
sin(x/2) = + √(1 - cos²(x/2)) = √[1/2 - 19/(2 √937)]
and by definition of tan,
tan(x/2) = sin(x/2) / cos(x/2) = 1/12 √[649/2 - 19 √937/2]
Just to be clear, the solutions are
<h3>
Answer: 9</h3>
===================================================
Explanation:
The area of the parallelogram is equal to the base times height. The formula to use is A = b*h. The height and base are always perpendicular to one another.
The base is some unknown variable b. Multiply the base by the height 15 to get 15*b which is equal to the area 135
Therefore, 15*b = 135
Divide both sides by 15 and we isolate b
15b = 135
15b/15 = 135/15
b = 9
So the base is 9
Check:
area = base*height = 9*15 = 135
so the answer is confirmed
side note: we never use the value 17 at all. It is likely put in there as a distraction.
A circle is 360
so we're going to set up a proportion
120 x
------ = ------
360 100
then cross multiply and divide
120 times 100=12000/360=33.3333333
so the answer is C. 33
I hope I've helped!
Answer:
370 stores
Step-by-step explanation:
Given data
initial number of stores P= 200
r= 8%
t= 1999-2007= 8 years
Let us apply the compound interest expression to find the final amount of stores
A= P(1+r)^t
A= 200(1+0.08)^8
A= 200(1.08)^8
A= 200*1.85
A=370
Hence the number of stores in 2007 is 370 stores
Answer:
8/26
Step-by-step explanation:
there are 8 blue out of a total of 26 in total
