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
Nar
malfutka [58]

Answer:27 divided by 3 to get 9 or add 3 repetitively to get 27 or 3x=27

Step-by-step explanation:

7 0
3 years ago
Amir has a $2 off coupon for his favorite sub shop. To get the deal, he must buy a 6” sandwich and chips, a soda, or a cookie. H
Igoryamba
His total would be $5.50

5.50+0.75+1.25= 7.50

7.50-2(the coupon) = $5.50 total
3 0
3 years ago
Read 2 more answers
Melinda and Marcus are saving money to purchase a present for a friend. Each friend starts with an amount and also saves a speci
Goshia [24]
Let's find the rates at which Melinda and Marcus are saving money and compare them. 
Based on the table, we can see that Melinda originally had $75. Then she got $135 in 5 weeks.  So the rate of saving money is (135–75)/5 = $12 per week.
This rate is unchanged for the next weeks. As we can see, she got $195 in the next 5 weeks. So she saved $60 more those 5 weeks, or the rate is $60/5 = $12 per week again. 

So Melinda saved $12 per week.
As for Marcus, the equation tells us that the rate of saving money is $14 which is the coefficient in front of x.

Hence, t<span>he rate at which Melinda is adding to her savings each week is 2$
less than the rate at which Marcus is adding to his savings each week.</span>
5 0
3 years ago
Read 2 more answers
The graph shows the number of paintballs a machine launches, y, in x seconds:
Goryan [66]
Fraction 4 over eighty
4 0
3 years ago
Read 2 more answers
a tram moved upward 9 meters per second for 63 seconds. what was the total change in the trams elevation
Ganezh [65]
After 63 seconds the tram moved 567 meters upward
8 0
3 years ago
Other questions:
  • What is an equivalent expression to 4+3(5+x)
    8·1 answer
  • Susan joined a video rental club . She paid an initiation fee of $12.75, and it cost $0.75 per video that she rented . Write an
    5·1 answer
  • Solve for m: m/5 + 3(m-1)/) = 2(m-3)
    5·2 answers
  • liz wants to buy her favorite musical group’s new cd. the cd costs $15.24, including tax. liz gives the store clerk a twenty-dol
    14·1 answer
  • Determine if the events listed are independent or dependent.
    9·1 answer
  • Graph y= 1/2x–3 . <br> Where would I put the points ?
    12·1 answer
  • Write -2x^2+3x-2 in the form a(X+p)^2 +q​
    6·1 answer
  • Need help, please 10 pts
    8·1 answer
  • I need help! I will give brainliest, if correct!
    12·2 answers
  • (f) A recipe calls for 1 1/2 cups of flour, 3/4 cup of white sugar, and 1/8 cup of brown sugar.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!