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xenn [34]
3 years ago
5

What is sin(4a) & cos(4a) if tan(a)=3

Mathematics
1 answer:
ratelena [41]3 years ago
6 0

Answer:

  • sin(4a) = -24/25
  • cos(4a) = 7/25

Step-by-step explanation:

Your calculator can tell you these values:

  sin(4a) = sin(4·arctan(3)) = -0.96 = -24/25

  cos(4a) = cos(4·arctan(3)) = 0.28 = 7/25

_____

Some useful trig identities are ...

  sin(2a) = 2tan(a)/(1 +tan(a)^2)

  cos(2a) = (1 -tan(a)^2)/(1 +tan(a)^2)

Filling in the given value for tan(a), we find ...

  sin(2a) = 2(3)/(1+3^2) = 6/10 = 3/5

  cos(2a) = (1 -3^2)/(1 +3^2) = -8/10 = -4/5

Now, double-angle formulas are useful:

  sin(4a) = 2sin(2a)cos(2a) = 2(3/5)(-4/5) = -24/25

  cos(4a) = 1 -2sin(2a)^2 = 1 -2(3/5)^2 = 7/25

The desired trig function values are sin(4a) = -24/25; cos(4a) = 7/25.

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Answer:

D. 144

Step-by-step explanation:

find the volume of the shipping container and divide it by the volume of a box.

2\frac{2}{3} × 1 × 2 = \frac{16}{3}

\frac{1}{3} × \frac{1}{3} × \frac{1}{3} = \frac{1}{27}

\frac{16}{3} divided by \frac{1}{27} is 144.

4 0
3 years ago
Bicycle started writing at 8 AM the diagram below shows the distance the bicycle had traveled at different times what was the bi
damaskus [11]
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7 0
3 years ago
Susan and Mark are standing at different places on a beach and watching a bird. The angles of elevation they make are 20º and 50
Mandarinka [93]

Answer:

The bird is 2.44km high

Step-by-step explanation:

Hello,

To solve this question, we need to understand how they are and we can only get this with a correct pictorial diagram.

See attached document for better understanding.

From the first diagram, we understand that the bird is between them and also on top of them.

Assuming Susan, Mark and the bird all form a triangle at each other and the bird at the top, we can divide the the triangle into two equal parts.

But before then, we should know that sum of angles in a triangle is equal to 180°

Therefore,

20° + 50° + b° = 180

70° + b = 180

b = 180° - 70°

b = 110°

Dividing angle b into two equal parts = 55° on each side.

See the last attached document for better illustration.

Using SOHCAHTOA, we can find the adjacent of the triangle which corresponds to the height of the bird.

We have opposite = 3.4km and we're looking for adjacent. We can use tangent of the angle to find the adjacent.

Tanθ = opposite / adjacent

Tan 55° = 3.5 / adj

Adjacent = 3.5 / tan55

Adjacent = 3.5 / 1.43

Adjacent = 2.44km

The height of the bird is 2.44km

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3 years ago
Forma de distribución del resultado obtenido por los componentes de una sociedad tomando en cuenta dos factores que intervienen,
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Reparto proporcional
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3 years ago
Which is true about the polynomial -8m3 11m?O It is a binomial with a degree of 2.O It is a binomial with a degree of 3.O It is
koban [17]
-8m^3 + 11m....notice that it has 2 terms....(-8m^3) and (11m). Having 2 terms makes it a binomial...if it would have had 3 terms, it would have been a trinomial. If it has only one variable, the degree is the highest exponent...so this has a degree of 3 since ^3 is the highest exponent.
so ur answer is : binomial with a degree of 3
3 0
3 years ago
Read 2 more answers
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