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goldenfox [79]
3 years ago
11

Lowering powers write in terms of first power of cosine. Cos^6

Mathematics
1 answer:
yaroslaw [1]3 years ago
4 0

The main identity you need is the double angle one for cosine:

\cos^2x=\dfrac{1+\cos2x}2

We get

\cos^6x=(\cos^2x)^3=\left(\dfrac{1+\cos2x}2\right)^3=\dfrac{(1+\cos2x)^3}8

Expand the numerator to apply the identity again:

\cos^6x=\dfrac{1+3\cos2x+3\cos^22x+\cos^32x}8

\cos^6x=\dfrac{1+3\cos2x+3\left(\frac{1+\cos2(2x)}2\right)+\cos2x\left(\frac{1+\cos2(2x)}2\right)}8

\cos^6x=\dfrac{1+3\cos2x+\frac32+\frac32\cos4x+\frac12\cos2x(1+\cos4x)}8

\cos^6x=\dfrac5{16}+\dfrac7{16}\cos2x+\dfrac3{16}\cos4x+\dfrac1{16}\cos2x\cos4x

Finally, make use of the product identity for cosine:

\cos2x\cos4x=\dfrac{\cos6x+\cos2x}2

so that ultimately,

\cos^6x=\dfrac5{16}+\dfrac7{16}\cos2x+\dfrac3{16}\cos4x+\dfrac1{32}\cos2x+\dfrac1{32}\cos6x

\cos^6x=\dfrac5{16}+\dfrac{15}{32}\cos2x+\dfrac3{16}\cos4x+\dfrac1{32}\cos6x

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In the New York State daily lottery game, a sequence of 4 (not necessarily different) digits in the range of 0-9 is selected at
devlian [24]

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50.40% probability that all 4 are different.

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A probability is the number of desired outcomes divided by the number of total outcomes.

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By the same logic, 7 possible digits for the fourth. So

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2 years ago
I’m confused on this one
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The answer is 42.

The question is asking for angle N. We know from the question that angle N is equal to angle E (Don't think about the scale factor because it only applies to the sides. They're just trying to trick you).

To find angle E:
79 + 6x + 11  + 7x - 14 = 180
Move numbers to the right side:
6x + 7x = 180 - 79 - 11 + 14
Combine like terms:
13x = 104
Divide both sides by 13:
x = 8
The formula for angle E:
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Plug in the 8:
7 \times 8 - 14 = 56 - 14 = 42
The angle measure of E is 42. So angle N is automatically 42 too.

To solidify, we can try to use the formula which they give us for angle N:
3x + 18 = 24 + 18 = 42
8 0
3 years ago
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