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vazorg [7]
3 years ago
8

Help

Physics
2 answers:
Ede4ka [16]3 years ago
7 0

<h2>sin (x + y) ≈ 0.58</h2>

<h3>Further explanation</h3>

Firstly , let us learn about trigonometry in mathematics.

Suppose the ΔABC is a right triangle and ∠A is 90°.

<h3>sin ∠A = opposite / hypotenuse</h3><h3>cos ∠A = adjacent / hypotenuse</h3><h3>tan ∠A = opposite / adjacent </h3>

There are several trigonometric identities that need to be recalled, i.e.

cosec ~ A = \frac{1}{sin ~ A}

sec ~ A = \frac{1}{cos ~ A}

cot ~ A = \frac{1}{tan ~ A}

tan ~ A = \frac{sin ~ A}{cos ~ A}

Let us now tackle the problem!

If sec (y) = 25/24 , then we can assume that :

adjacent side = 24 cm

hypotenuse = 25 cm

opposite side = \sqrt{25^2 - 24^2} = 7 ~ cm

sin (y) = opposite / hypotenuse = 7/25

If sin (x) = 1/3 , then we can assume that :

opposite side = 1 cm

hypotenuse = 3 cm

adjacent side = \sqrt{3^2 - 1^2} = \sqrt{8} ~ cm

cos (x) = adjacent / hypotenuse = \sqrt{8}/3 = \frac{2\sqrt{2}}{3}

\sin (x + y) = \sin x ~ \cos y + \cos x ~ \sin y

\sin (x + y) = \frac{1}{3} \times \frac{24}{25} + \frac{2\sqrt{2}}{3} \times \frac{7}{25}

\large {\boxed {\sin (x + y) = \frac{24 + 14\sqrt{2}}{75} \approx 0.58} }

<h3>Learn more</h3>
  • Calculate Angle in Triangle : brainly.com/question/12438587
  • Periodic Functions and Trigonometry : brainly.com/question/9718382
  • Trigonometry Formula : brainly.com/question/12668178

<h3>Answer details</h3>

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle

Blizzard [7]3 years ago
6 0
We can approach this in another way.
We know that sin(∅) = height / hypotenuse.

Thus, for x, height is 1 and hypotenuse is 3. Using Pythagoras theorem,
3² = 1² + b²
b = √8
cos(x) = b/hypotenuse
cos(x) = √8 / 3

Now, lets consider y:
sec(y) = 1 / cos(y) = 1 / base / hypotenuse = hypotenuse / base
The hypotenuse is 25 and the base is 24. We again apply Pythagoras theorem to find the third side, which works out to be:
height = 7
sin(y) = height / hypotenuse
sin(y) = 7/25

Now, sin(x + y) =
sin(x)cos(y) + sin(y)cos(x)
= (1/3)(24/25) + (√8 / 3)(7/25)
= 8/25 + 7√8/75
= (24 + 14√2) / 75
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What phase difference between two identical traveling waves, moving in the same direction along a stretched string, results in t
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Answer:

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This is note the complete question, the complete question is:

One of the lousy things about getting old (prepare yourself!) is that you can be both near-sighted and farsighted at once. Some original defect in the lens of your eye may cause you to only be able to focus on some objects a limited distance away (near-sighted). At the same time, as you age, the lens of your eye becomes more rigid and less able to change its shape. This will stop you from being able to focus on objects that are too close to your eye (far-sighted). Correcting both of these problems at once can be done by using bi-focals, or by placing two lenses in the same set of frames. An old physicist instructor can only focus on objects that lie at distance between 0.47 meters and 5.4 meters.

Assume that the physics instructor would like to have normal visual acuity from 21 cm out to infinity and that his bifocals rest 2.0 cm from his eye. What is the refractive power of the portion of the lense that will correct the instructors nearsightedness?

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when an object is held 21 cm away from the instructor's eyes, the spectacle lens must produce 0.47m ( the near point) away.

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i.e 45 cm from the spectacle lens since the spectacle lens is 2cm away from the eye.

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object distance  d₀ = 21 - 2 = 19cm = 0.19m

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