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3 years ago

Help me please I need to answer this

Mathematics

1 answer:

melamori03 [73]3 years ago

5 0

Answer:

three shirts an hour

Step-by-step explanation:

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Sinx + siny=a<br> cosx + cosy=b<br> Find cos(x+y/2)

romanna [79]

Using the addition rule of the Sine function and the Cosine function, we obtain $\cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}$ .

<h3>What are the formulas for (sin x + sin y) and (cos x + cos y)?</h3>

The formula for the addition of two Sine functions ( $\sin x+\sin y$ ) is $\sin x + \sin y = 2\sin\frac{x+y}{2}\cos\frac{x-y}{2}$ .
The formula for the addition of two Cosine functions ( $\cos x+\cos y$ ) is $\cos x + \cos y = 2\cos\frac{x+y}{2}\cos\frac{x-y}{2}$ .

Given that

$\sin x + \sin y = a\\\cos x + \cos y = b$

Then using the above formulas, we get:

$2\sin\frac{x+y}{2}\cos\frac{x-y}{2}=a$ (1)

$2\cos\frac{x+y}{2}\cos\frac{x-y}{2}=b$ (2)

Dividing the equation (1) by (2), we get:

$\dfrac{\sin\dfrac{x+y}{2}}{\cos\frac{x-y}{2}}=\dfrac{a}{b}\\\Longrightarrow \tan\dfrac{x+y}{2}=\dfrac{a}{b}$ (3)

Now, we know that $\cos\theta=\dfrac{1}{\sqrt{1+\tan^2\theta}}$ .

Thus, using the above formula, we get from (3):

$\cos\dfrac{x+y}{2}=\dfrac{1}{\sqrt{1+\tan^2\dfrac{x+y}{2}}}\\\Longrightarrow \cos\dfrac{x+y}{2}=\dfrac{1}{\sqrt{1+\dfrac{a^2}{b^2}}}\\\Longrightarrow \cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}$

Therefore, using the addition rule of the Sine function and the Cosine function, we obtain $\cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}$ .

To know more about Sine and Cosine functions, refer: brainly.com/question/27728553

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3 0

2 years ago

Sum of 34908 and 12765?

iren2701 [21]

Answer:

47,673

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Anyone 100% know dis answer

siniylev [52]

Answer:

Rotational symmetry

Step-by-step explanation:

The rectangle rotated 180 degrees to get the transformed rectangle.

4 0

3 years ago

Why are 1 4 9 16 and 25 called perfect squares

olga nikolaevna [1]

Perfect squares can be divided and multiplied by the same number to get the same number. For example 25/5=5. 5*5=25.
4/2=2, 2*2=4
1/1=1, 1*1=1
9/3=3, 3*3=9
16/4=4, 4*4=16.
Hence the perfect squares.

4 0

3 years ago

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How do I find the unit rate?<br> $253 for 20 hours

DIA [1.3K]

Divide 253 by 20 to get the unit rate.
We get 12.65
So our unit rate is; $12.65 per hour

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4 years ago