Answered: How is sin-1 used in the real world? Im…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

How is sin^-1 used in the real world? Im having a hard time grasping the concept of how to use it, I understand that its for only a potion of of the sine wave (1 to -1) and it somehow "undoes" sin simular to how x²can undo a squair root, but why would I want to undo sin? I have a hard time grasping abstract math in a math class but no problem grasping math in a phisics class because my brain has a "place" to put the concept and what to realate it to. For example a²+b²=c²is meaningless and abstract untill its applied to a triangle then it has meaning and can be remembered. Thank you for your time.

Expert Solution

Step 1: Step 1:

The inverse sine function, often denoted as $s i n to the power of negative 1 end exponent$ or arcsin, is used to find the angle whose sine equals a given value. In other words, it helps you "undo" the sine operation and find the original angle. Here's how it is used in various real-world scenarios:

Geometry and Trigonometry: In geometry and trigonometry, you often encounter problems involving right triangles or other shapes where you need to find angles. For example, if you know the length of two sides of a right triangle, you can use arcsin to find one of the angles. This is essential for tasks like surveying land or constructing buildings.

Physics: In physics, arcsin is used in many situations involving oscillations, waves, and rotations. For instance, when analyzing simple harmonic motion, you might need to find the initial phase angle or the angle at which a pendulum is released to achieve a specific amplitude.

Engineering: Engineers use arcsin to calculate angles in various applications, such as determining the angles for robotic arm movements or calculating the angle at which a satellite dish should be positioned to receive signals.

Computer Graphics: In computer graphics and animation, arcsin is used to create realistic movements and animations. It's crucial for things like simulating the motion of a character's joints or controlling the angles of camera rotations.