All categories

2 years ago

Find sin(x/2), cos (x/2), and tan(x/2) from the given information.

Mathematics

1 answer:

zhannawk [14.2K]2 years ago

6 0

Step-by-step explanation:

sin(x/2) = sqrt((1 - cos(x))/2)

cos(x/2) = sqrt((1 + cos(x))/2)

tan(x/2) = sin(x/2)/cos(x/2)

sin(x) = 15/17

so, we can assume the Hypotenuse of the right-angled triangle is 17, the vertical leg is 15.

via Pythagoras we get the 3rd, horizontal side :

17² = 15² + side²

289 = 225 + side²

64 = side²

side = 8

cos(x) = 8/17

sin(x/2) = sqrt((1 - 8/17)/2) = sqrt(9/34) = 3/sqrt(34) =

= 0.514495755...

cos(x/2) = sqrt((1 + 8/17)/2) = sqrt(25/34) = 5/sqrt(34) =

= 0.857492926...

tan(x/2) = 3/sqrt(34) / 5/sqrt(34) = 3/sqrt(34) × sqrt(34)/5 =

= 3/5 = 0.6

You might be interested in

William Arsenio is remodeling his home in order to save money he is upgrading the plumbing himself he needs 27 pieces of copper

Reptile [31]

Answer:

Yes.

2 feet

Step-by-step explanation:

Pieces of copper that Arsenio needs in total = 27 pieces

Length of each piece of copper tubing that he needs = 2/9 foot

Length of available tubing = 8 foot

Since, the length of each piece is 2/9 foot, the length of 27 pieces would be:

$\frac{2}{9} \times 27 = 6$

This means, Arsenio needs 6 feet in total for the copper tubing. Since he got 8 feet in total, he has sufficient amount of tubing available.

After making the 27 pieces, he will be left with 8 - 6 = 2 feet of tubing.

6 0

3 years ago

15 POINTS PLEASE HELP

Anika [276]

4. x^10

5. x^3

I hope this helped! Mark me Brainliest! :) -Raven❤️

3 0

3 years ago

How many quarts of pure antifreeze must be added to 5 quarts of a 40% antifreeze solution to obtain a 50% antifreeze solution

GarryVolchara [31]

Answer:

2 quarts of 100% antifreeze.

Step-by-step explanation:

5 quarts/ .40 * x/ 1

.40x= 5

x=2

6 0

3 years ago

If the base of a square pyramid is 9 centimeters, and it has a volume of 324 cubic centimeters, what is the height of the pyrami

masha68 [24]

The volume (V) of a pyramid is found using the formula

V = $\frac{1}{3}$ × area of base × height(h)

area of base = 9² = 81 ← area of a square, hence

324 = $\frac{1}{3}$ × 81 × h = 27h ( divide both sides by 27 )

h = $\frac{324}{27}$ = 12 → A

3 0

3 years ago

Assume you know that a hot-air balloon is currently inflated with a certain amount of air and that the amount is a percent of th

Gemiola [76]

Answer:

<u>Percent air is calculated as:</u>

Percent air = Current amount/Total amount *100

<u>Solve for total amount of air:</u>

Total amount = Current amount / Percent air * 100

Substitute the values in hand to get the answer

3 0

3 years ago