Evaluate. sin^-1(sin(π)/(5))

Name: Problem 41, Chapter 7: Algebra and Trigonometry
Uploaded: 2020-07-08T01:38:27-08:00
Duration: 49 s
Channel: Ankit Gupta
Description: Evaluate. sin^-1(sin(π)/(5))

step 1 We have to find the value of sine inverse, sine by 5. Now we know the function sine inverse x an

Question

Evaluate. $$\sin ^{-1}\left(\sin \frac{\pi}{5}\right)$$

   Evaluate.
$$\sin ^{-1}\left(\sin \frac{\pi}{5}\right)$$

Algebra and Trigonometry

Judith A. Beecher,… 4th Edition

Chapter 7, Problem 41

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Solved by Expert Ankit Gupta

07/08/2020

Step 1

Step 1: We are given the expression $\sin ^{-1}\left(\sin \frac{\pi}{5}\right)$ and we need to evaluate it. Show more…

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Evaluate. $$\sin ^{-1}\left(\sin \frac{\pi}{5}\right)$$

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Key Concepts

Inverse Trigonometric Functions

Inverse trigonometric functions, such as the arcsine, give the angle whose trigonometric function equals a given number. They are the inverse operations to the usual trigonometric functions, allowing us to determine an angle when its sine, cosine, or tangent value is known.

Principal Value Branch

The principal value branch is the restricted range of an inverse trigonometric function that ensures it is single-valued. For example, the arcsine function returns values only in the interval [-?/2, ?/2], even though the sine function is periodic, ensuring a unique angle is obtained for each sine value.

Periodicity of the Sine Function

The sine function is periodic, meaning its values repeat in regular intervals (with a period of 2?). However, when using the inverse sine function, we work within a single period defined by the principal branch, which means the output is the unique angle within that set range corresponding to the sine value.

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