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const2013 [10]
3 years ago
15

Let f(x) be a polynomial such that f(cos θ) = cos(4) θ for all θ. Find f(x). (This is essentially the same as finding cos(4) θ i

n terms of cos θ we structure the problem this way so that you can answer as a polynomial. Be sure to write your polynomial with the terms in order of decreasing degree.)
Mathematics
1 answer:
Galina-37 [17]3 years ago
5 0

Answer:

f(x) = 8x⁴-8x²+1

Step-by-step explanation:

I will assume that f(cos θ) = cos(4θ). Otherwise, f would not be a polynomial. lets divide cos(4θ) in an expression depending on cos(θ). We use this properties

  • cos(2a) = cos²(a) - sin²(b)
  • sin(2a) = 2sin(a)cos(a)
  • sin²(a) = 1-cos²(a)

cos(4θ) = cos(2 * (2θ) ) = cos²(2θ) - sin²(2θ) = [ cos²(θ)-sin²(θ) ]² - [2cos(θ)sin(θ)]² = [cos²(θ) - ( 1 - cos²(θ) ) ]² - 4cos²(θ)sin²(θ) = [2cos²(θ)-1]² - 4cos²(θ) (1 - cos²(θ) ) = 4 cos⁴(θ) - 4 cos²(θ) + 1 - 4 cos²(θ) + 4 cos⁴(θ) = 8cos⁴(θ) - 8 cos²(θ) + 1

Thus f(cos(θ)) = 8 cos⁴(θ) - 8 cos²(θ) + 1, and, as a result

f(x) = 8x⁴-8x²+1.

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Step-by-step explanation:

5 0
3 years ago
Which pair shows equivalent expressions?
AVprozaik [17]
The 3rd one because the rest you would have to distribute them and for the 3rd one it’s the same
3 0
3 years ago
Ian has 120 folders to file. So far, he has filed 36 of the folders. What percent of the folders does he have left to file?
Gwar [14]
The answer is A
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3 0
3 years ago
P( rolling a number greater than 2 and the coin landing on heads or tails)
irina [24]

The value of P(rolling a number greater than 2 and the coin landing on heads or tails) is 4/6

<h3>How to determine the probability?</h3>

The given parameters are:

Objects = Dice and Coin

The sample space of the objects are:

Dice = {1, 2, 3, 4, 5, 6}

Coin = {Head, Tail}

From the above sample spaces, we have:

P(Rolling a number greater than 2) = 4/6

P(Coin landing on heads or tails)  = 1

The required probability is then calculated as:

P(rolling a number greater than 2 and the coin landing on heads or tails) = P(Rolling a number greater than 2) * P(Coin landing on heads or tails)

Substitute the known values in the above equation

P(rolling a number greater than 2 and the coin landing on heads or tails) = 4/6 * 1

Evaluate the product

P(rolling a number greater than 2 and the coin landing on heads or tails) = 4/6

Hence, the value of P(rolling a number greater than 2 and the coin landing on heads or tails) is 4/6

Read  more about probability at:

brainly.com/question/24756209

#SPJ1

3 0
2 years ago
If I triple four and subtract 2 each day how many days till I have zero
dangina [55]
Triple 4 is just 12
4X3=12
And so you can then divide by 2 because 2 each day(you could also just keep subtracting). Either way, you get 6 days
3 0
3 years ago
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