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3 years ago

Write the expression in terms of sin x and cos x only. sin(2x)+cos(3x)

2 answers:

5 0

Sin2x=2sinxcosx, cos2x=1-2sin^2x
sin(2x)+cos(3x)=2sinxcosx+cos(x+2x)
cos(x+2x)=cosx(1-2sin^2(x))-sinx2sinxcosx
sin(2x)+cos(3x)=2sinxcosx(1-sinx)+cosx(1-2sin^2(x))

Alisiya [41]3 years ago

5 0

Use the following identities:
$\sin{2x}=2\sin{x}\cos{x}\\ \cos{2x}=\cos^2{x}-\sin^2{x} \\ \cos{(x+y)}=\cos{x}\cos{y}-\sin{x}\sin{y}$

$\sin{2x}+\cos{3x} \\=2\sin{x}\cos{x}+\cos{(2x+x)} \\=2\sin{x}\cos{x}+\cos{2x}\cos{x}-\sin{2x}\sin{x} \\=2\sin{x}\cos{x}+(\cos^2{x}-\sin^2{x})\cos{x}-2\sin{x}\cos{x}\sin{x} \\=2\sin{x}\cos{x}+\cos^3{x}-\sin^2{x}\cos{x}-2\sin^2{x}\cos{x} \\=2\sin{x}\cos{x}+\cos^3{x}-3\sin^2{x}\cos{x} 
\\=\sin{x}\cos{x}(2+\cos^2{x}-3\sin{x})$

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Please give a full explanation and I will give you brainlest

andrew-mc [135]

Answer:

w = 33

Step-by-step explanation:

w ÷ 3.3 = 10

multiply both sides by 3.3:

w ÷ 3.3 x 3.3 = 10 x 3.3

⇒ w = 33

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2 years ago

How many points do you need in order to name a ray? O one four о three two

yawa3891 [41]

<h3>Answer: D) Two</h3>

You need the starting point, and another point that helps direct where the ray is aimed. Call these two points A and B.

Saying "Ray AB" means we extend a line through AB such that the line goes forever through B and beyond B, but we do not do the same for point A. The point A is effectively a cliff where no road goes on the other side of it. Check out the diagram below to see what I mean. The arrow means the line goes on forever in that direction.

5 0

2 years ago

Read 2 more answers

A hexagon has equal side lengths and angle measures. How many reflectional symmetry does the regular hexagon have?.

MatroZZZ [7]

The regular hexagon has 6 reflectional symmetries.

A regular hexagon has 6 congruent sides.

The number of sides of a polygon is the number of reflectional symmetry the polygon have.

Since the number of congruent sides of a regular hexagon is 6, then the regular hexagon has 6 reflectional symmetries.

Read more about reflectional symmetry at:

brainly.com/question/24584937

3 0

2 years ago

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Mark bought refreshments. Sandwiches were 2.50 each and bottles of water were $1.25 each. He spent $356.25 on a total of 180 ite

Over [174]

First you have to write the equation. in the scenario, use standard form.
Ax+By=C
plug the numbers in. A=2.50, B=1.25, and C is the total, 356.25. the 180 doesn't come in quite yet.
your equation is 2.50x+1.25y=356.25. now, since they only bought 180 items, you can't go past that.

I am sorry, but I am about to leave for school, and therefore do not have enough time to answer the last of your question. I hope the part I could answer has helped you.

7 0

3 years ago

2067 Supp Q.No. 2a Find the sum of all the natural numbers between 1 and 100 which are divisible by 5. Ans: 1050

Alborosie

Answer:

1050

Step-by-step explanation:

Natural Numbers are positive whole numbers. They aren't negative, decimals, fractions. We can just divide 5 into 100 to find how many natural numbers go up to 100 and just add them but that is just to much.

There is a easier method.

E.g: Natural Numbers that are divisible by a Nth Number. is the same as adding the Nth Numbers to a multiple of that Nth Term. For example, let say we need to find numbers divisible by 2. We know that 4 is divisible by 2 because 4/2=2. We can add the Nth numbers which is 2 to 4. 4+2=6. And 6 is divisible by 2 because 6/2=3. We can call this a arithmetic series. A series which has a pattern of adding a common difference

Back to the problem, we can use the sum of arithmetic series formula,

$y = x( \frac{z {}^{1} + {z}^{n} }{2} )$

Where x is the number of terms in our sequence. Z1 is the fist term of our series. ZN is our last term. And y is the sum of all of the terms

The first term is 5, the numbers of terms being added is 20 because 100/5=20. The last term is 100.

$y = 20( \frac{5 + 100}{2} )$

$y = 20( \frac{105}{2} )$

$y = 1050$

5 0

2 years ago