Chapter 2: Q15P (page 71)

Verify each of the following by using equations (11.4), (12.2), and (12.3).
siniz = i sin z

Short Answer

Expert verified

The equation sinh iz = i sin zis verified using the equations (11.4), (12.2) and (12.3).

Step by step solution

Given Information

Givenequationis sinh iz= i sin z

Definition of Hyperbolic Function.

The term "Hyperbolic Function" refers to the relationship between a point on a hyperbola's distance from its origin and its coordinate axes, expressed as a function of an angle.

Use exponential form to expand the equation

Given the equation is sinh iz = isin z.

The exponential form of the given equation is,

$\sin (z) = \frac{e^{(z)} - e^{(- z)}}{2 i}$ .

….(1)

Let $z \to z i$ than sin (iz) $= \frac{e^{(z i . i)} - e^{(- z i . i)}}{2 i}$ .

Solve sin (iz) to prove the given equation.

$\sin (i z) = \frac{e^{(z i)} - e^{(- z i)}}{2 i}$

Multiply numerator and denominator by i.

$\sin h (i z) = \frac{i}{i} \times \frac{e x p (z i) - e (- z i)}{2} \sin h (i z) = \frac{i [e x p (z i) - e x p (- z i)]}{2 i} \sin h (i z) = \frac{i}{i} \times \frac{e x p (z i) - e (- z i)}{2} \sin h (i z) = i \sin (z)$

Hence, the equation is verified.

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Verify each of the following by using equations (11.4), (12.2), and (12.3).
siniz = i sin z

Short Answer

Step by step solution

Given Information

Definition of Hyperbolic Function.

Use exponential form to expand the equation

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Verify each of the following by using equations (11.4), (12.2), and (12.3).siniz = i sin z

Short Answer

Step by step solution

Given Information

Definition of Hyperbolic Function.

Use exponential form to expand the equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Engineering Physics

Solid State Physics

Further Mechanics and Thermal Physics

Atoms and Radioactivity

Work Energy and Power

Particle Model of Matter

Study anywhere. Anytime. Across all devices.

Verify each of the following by using equations (11.4), (12.2), and (12.3).
siniz = i sin z