Evaluate sin(5 π)/(12)

Name: Problem 46, Chapter 1: Thomas Calculus
Uploaded: 2019-04-30T23:35:00-08:00
Duration: 1 min 23 s
Channel: Matt Just
Description: Evaluate sin(5 π)/(12)

step 1 Okay, so we want to evaluate sine of 5 pi over 12. So this is sine of pi over 6 plus pi over 4.

Question

Evaluate $\sin \frac{5 \pi}{12}$

   Evaluate $\sin \frac{5 \pi}{12}$

Thomas Calculus

George B. Thomas Jr. 14th Edition

Chapter 1, Problem 46

Instant Answer

Solved by Expert Matt Just

04/30/2019

Step 1

So, we have $\frac{5 \pi}{12} = \frac{\pi}{6} + \frac{\pi}{4}$. Show more…

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Evaluate $\sin \frac{5 \pi}{12}$

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Key Concepts

Standard Angles

Standard angles refer to specific angles like 30°, 45°, and 60° (or their radian equivalents), for which the trigonometric function values are well-known or easily derived. Recognizing these angles and their corresponding sine and cosine values is crucial for using trigonometric identities effectively.

Angle Sum and Difference Identities

Angle sum and difference identities allow the evaluation of trigonometric functions for non-standard angles by expressing them in terms of the functions of standard angles. These identities are essential tools for breaking down complex angles into simpler ones whose sine and cosine values are known.

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, relate the angles of a triangle to ratios of its sides. They are fundamental in understanding periodic phenomena and the geometry of the unit circle, and they play a crucial role in many areas of mathematics and applied sciences.

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