1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
sergij07 [2.7K]
3 years ago
7

If cos x= 5/13 and sin x <0 find cos (x/2) and sin (2x)

Mathematics
1 answer:
taurus [48]3 years ago
4 0
We know that

if cos x is positive
and
sin x is negative
so
the angle x belong to the IV quadrant

cos x=5/13
we know that
sin²x+cos²x=1-------> sin²x=1-cos²x------> 1-(5/13)²---> 144/169
sin x=√(144/169)-------> sin x=12/13
but remember that x is on the IV quadrant
so
sin x=-12/13

Part A) <span>cos (x/2)
cos (x/2)=(+/-)</span>√[(1+cos x)/2]
cos (x/2)=(+/-)√[(1+5/13)/2]
cos (x/2)=(+/-)√[(18/13)/2]
cos (x/2)=(+/-)√[36/13]
cos (x/2)=(+/-)6/√13-------> cos (x/2)=(+/-)6√13/13
the angle (x/2) belong to the II quadrant
so
cos (x/2)=-6√√13/13

the answer Part A) is 
cos (x/2)=-6√√13/13

Part B) sin (2x)
sin (2x)=2*sin x* cos x------> 2*[-12/13]*[5/13]----> -120/169

the answer Part B) is 
sin(2x)=-120/169
You might be interested in
. Keith plans on eating 1 cup of tuna per day for five days. How much tuna does he need? Are 4 cans enough?
vovikov84 [41]
He has too much for 4 cans. He has 5 3/5
cups.
7 0
3 years ago
Read 2 more answers
. Tommy gives baseball cards to four of his friends. He gives Kiana 3 cards less than he gives Gary.
Licemer1 [7]
We need to write system of equations for this problem. Reading text we write 1 equation by 1.
first lets name our variables
x - Kiana cards
y - Gary cards
z - Monty cards
m - Willa cards

x = y-3         which we can write as y = x+3
z = x + 7
m = 2z
x + y + z + m = 74

I think easiest way to solve this is to express all variables in last equation and solve for x.
x + x+3 + x + 7+ 2x + 14= 74
5x = 50
x = 10
now we just calculate cards given to each friend

y = 13
z = 17
m = 34
7 0
3 years ago
Which situation could not represent a proportional relationship?
Natasha_Volkova [10]
Megan bought a fridge for $499 plus $100 delivery fee is not a proportional relationship.
7 0
3 years ago
Read 2 more answers
How many cubic feet of water can the following in ground swimming pool hold
guapka [62]

Answer:

do length times width times height and see what you get if your answer is not on there split the figure into 2 shapes and do l*w*h to both and add you 2 figures together then see if you have your answer.

Step-by-step explanation:

do length times width times height and see what you get if your answer is not on there split the figure into 2 shapes and do l*w*h to both and add you 2 figures together then see if you have your answer. hope that helps!

3 0
3 years ago
A student used his place value chart to show a number. After the teacher instructed him to divide his number by 100,the chart sh
NeX [460]

When you divide by 100 you are essentially moving the decimal of the number two places to the left. In undoing this you would have to move the decimal of the number two places to the right.

28.003 would then turn into 2,800.3

Unfortunately I cannot draw a chart on here but that is the best I can do.

5 0
3 years ago
Read 2 more answers
Other questions:
  • Drag and drop a statement or reason to each box to complete the proof.
    5·1 answer
  • Question 5 of 5
    10·1 answer
  • sharon is 54 inches tall. A tree in her backyard is 5 times as tall as she is. The floor of her treehouse is at a height that is
    10·2 answers
  • Four less than the product of one and a number x.
    11·1 answer
  • 4 (2y+y) - 6 (4y+3y)
    14·1 answer
  • Identify the incorrect statement A. Alpha and beta particles pose little or no hazard to human health. B. Cosmic rays are a form
    9·1 answer
  • Please help me thank you I appreciate it
    6·2 answers
  • Algebra help!!! giving brainliest and you’ll get 20 points rather than 10!!! (asap please)
    9·2 answers
  • What is green and blue? HELP
    5·1 answer
  • Win bakes fruit bars in a pan shaped like a rectangular prism. The volume of the pan is 120 cubic inches. The length of the pan
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!