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
barxatty [35]
2 years ago
15

Simplify x = cos[2 arcsin(3/5)]. -7/25 7/25 4/5

Mathematics
1 answer:
Marina CMI [18]2 years ago
5 0

Answer:

7/25

Step-by-step explanation:

Let \theta= \arcsin(\frac{3}{5}) so we have x=\cos(2\theta)

As \cos(2\theta)=\cos^2\theta-\sin^2\theta, we'll have \cos[2\arcsin(\frac{3}{5})]=\bigr[\cos(\arcsin(\frac{3}{5}))\bigr]^2-\bigr[(\sin(\arcsin(\frac{3}{5}))\bigr]^2

To determine \cos(\arcsin(\frac{3}{5})), construct a right triangle with an opposite side of 3 and a hypotenuse of 5. This is because since \theta=\arcsin(\frac{3}{5}), then \sin\theta=\frac{3}{5}=\frac{\text{Opposite}}{\text{Hypotenuse}}. If you recognize the Pythagorean Triple 3-4-5, you can figure out that the adjacent side is 4, and thus, \cos\theta=\frac{4}{5}=\frac{\text{Adjacent}}{\text{Hypotenuse}}. This means that \cos(\arcsin(\frac{3}{5}))=\frac{4}{5}.

Hence, \cos[2\arcsin(\frac{3}{5})]=(\frac{4}{5})^2-(\frac{3}{5})^2=\frac{16}{25}-\frac{9}{25}=\frac{7}{25}

You might be interested in
NEED URGENT HELP
AnnyKZ [126]

Answer:

32.5

Step-by-step explanation:

If CED is 65, then AEB is 65, therefore we can calculate that CEA is 115 because 180 - 65 = 115. Then we do 180 - 115 = 65 which is the sum of angles ACE and CAE so 65 / 2 = 32.5 which is CAE.

Hope this helped!

8 0
3 years ago
The Rawlins family has travelled 600 km on their vacation. This has taken them 8 hours. If they continued at the same rate, how
spin [16.1K]

Answer:

B. 28 hours

Step-by-step explanation:

GIVEN :- <em>Time taken by family to travel 600 km is 8 hours</em>

CALCULATIONS :-

<em>To calculate the time to travel 2100 km, we need to calculate distance traveled in 1 hour</em>

<em>Distance traveled in 1 hour = 600 km ÷ 8</em>

<em>                                              = 75 km</em>

<em>Time required to travel 2100 km = 2100 ÷ 75</em>

<em>                                                         = </em><em>28 hours</em>

Therefore time required to travel 2100 km is 28 hours.


6 0
3 years ago
-1/4x+2y=28 find the x and y intercept
Advocard [28]
The y intercept is (0, 14) and the x intercept is (-112,0) all you have to do is just make y zero if you are trying to solve for x and the same for the x if you are trying to solve for y.
8 0
3 years ago
The tree house. Juanita is building is two two wholes and 2 1 / 2 ft from the ground the tree house that Rosa is building is fiv
Molodets [167]

Answer: 2/21 hope this helps : )

Step-by-step explanation: ok the way you do this s 21/2 times five then simplify, 5 is the GCF of 105 and 10 and when you simplify you get 21/2 flip the denominator with the divisor and you get 2/21  

5 0
2 years ago
Both windows are congruent. What is the combined area of the two windows?
Gnom [1K]
The area of the triangle is 3 because b•h/2, and the area of the rectangle is 3 because l•w, added together that equals 6, and doubled that equals 12. So I think the answer is C, 12 square feet.
7 0
3 years ago
Read 2 more answers
Other questions:
  • You plant a tree that is 36 inches tall. After one year, the tree is 43 inches tall. Write an expression which describes the per
    6·2 answers
  • In the number 4,118, how does the value represented by the 1 in the hundreds place compare with the value represented by the 1 i
    9·1 answer
  • What is the product of 379 and 8
    10·2 answers
  • What is the slope of a line <br> parallel to the line 4x – 3y = 16?
    7·2 answers
  • What is the answer for -|-5x(-7)|​
    8·2 answers
  • A distance of 150 km was covered by a motorcyclist traveling at an average speed of 75 km/h, by a bus at 60 km/h, a truck at 50
    15·1 answer
  • Cassie received a 20%-off coupon and a $10-off coupon from a department store. She visits the department store during a tax-free
    11·1 answer
  • Can anyone help me with this<br> Given an = −11n + 3 find the 100th term.
    14·1 answer
  • PLEASE HELP<br> Which is the function represented by the table?
    11·1 answer
  • Which facts are true for the graph of the function below? Check all that apply.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!