Answered: Evaluate and draw picture sin(4pi/3)

Name: Evaluate and draw picture sin(4pi/3)
Uploaded: 2024-03-20T06:46:55.000Z
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Description: Evaluate and draw picture sin(4pi/3)

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Evaluate and draw picture

sin(4pi/3)

Expert Solution

Step 1

GIVEN DATA : Expression $S i n (\frac{4 π}{3})$

TO FIND : Evaluate and draw the picture of the given expression

Given expression $S i n (\frac{4 π}{3})$

Write $S i n (\frac{4 π}{3})$ as $S i n (π + \frac{π}{3})$

$S i n (\frac{4 π}{3})$ $= S i n (π + \frac{π}{3})$ $(1)$

Step 2

Apply the summation identity of $\sin e$ $: s i n (a + b) = s i n (a) c o s (b) + s i n (b) c o s (a)$

$S i n (π + \frac{π}{3}) = S in (π) C os (\frac{π}{3}) + S i n (\frac{π}{3}) C o s (π)$ $(2)$

Using the trivial identity of

$S in (π) = 0 C os (\frac{π}{3}) = \frac{1}{2} S i n (\frac{π}{3}) = \frac{\sqrt{3}}{2} C o s (π) = (- 1)$

Use these identity in equation $(2)$

$S i n (π + \frac{π}{3}) = (0) (\frac{1}{2}) + (\frac{\sqrt{3}}{2}) (- 1)$

$S i n (π + \frac{π}{3}) = - (\frac{\sqrt{3}}{2})$

$S i n (\frac{4 π}{3}) = - (\frac{\sqrt{3}}{2})$

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