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Sergio039 [100]
3 years ago
6

{ TOPIC -- TRIGONOMETRIC IDENTITIES }

Mathematics
1 answer:
UkoKoshka [18]3 years ago
8 0
LHS ⇒ RHS:
Identities:
[1] cos(2A) = 2cos²(A) - 1 = 1 - 2sin²(A)
[2] sin(2A) = 2sin(A)cos(A)
[3] sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
[4] cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

cos(x) - cos(x + 2Θ)
= cos(x) - (cos(x)cos(2Θ) - sin(x)sin(2Θ))    [4]
= cos(x) - cos(x)(1 - 2sin²(Θ)) + sin(x)(2sin(Θ)cos(Θ))    [1] [2]
= cos(x) - cos(x) + 2sin²(Θ)cos(x) + 2sin(Θ)sin(x)cos(Θ)
= 2sin²(Θ)cos(x) + 2sin(Θ)sin(x)cos(Θ)
= 2sin(Θ)(sin(Θ)cos(x) + sin(x)cos(Θ))
= 2sin(Θ)sin(x + Θ)
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andreev551 [17]

According with the definition of translation, we conclude that the equations of graphs M and N are m(x) = f(x - 5) and n(x) = f(x) - 2, respectively.

<h3>How to apply translations on a given function</h3>

<em>Rigid</em> transformations are transformation such that the <em>Euclidean</em> distance of every point of a function is conserved. Translations are a kind of <em>rigid</em> transformations and there are two basic forms of translations:

Horizontal translation

g(x) = f(x - k), k ∈ \mathbb {R}     (1)

Where the translation goes <em>rightwards</em> for k > 0.

Vertical translation

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Where the translation goes <em>upwards</em> for k > 0.

According with the definition of translation, we conclude that the equations of graphs M and N are m(x) = f(x - 5) and n(x) = f(x) - 2, respectively.

To learn more on translations: brainly.com/question/17485121

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Solve for x and y 5x + 3y=35, 2x+4y=28​
Tatiana [17]
The answer would be:

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3 years ago
Read 2 more answers
Help me I have no idea how to do 18
sleet_krkn [62]

First, subtract px2 from both sides.

Now you have:

x3 - px2 = (1 - p) x1

Next, divide both sides by (1 - p)

So now you have

x3 - px2/(1 - p) = x1

...as your final answer


*You can decide if you want to leave the parenthesis in your final answer, I left them there so it could be visible where I put them. :)

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3 years ago
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