a. Answer The final answer is sin ( 7 π 6 − π 3 ) = 1 2 Explanation Given information :The given expression is sin ( 7 π 6 − π 3 ) Using sum and difference formula sin ( A − B ) = sin A . cos B − cos A . sin B We have sin ( 7 π 6 − π 3 ) = sin ( 7 π 6 ) . cos ( π 3 ) − cos ( 7 π 6 ) . sin ( π 3 ) = − 1 2 . 1 2 + 3 2 . 3 2 = − 1 4 + 3 4 = 1 2 b. To determine To find :To find the exact value of the expression sin 7 π 6 − sin π 3 . Answer The final answer is sin 7 π 6 − sin π 3 = − ( 1 + 3 ) 2 Explanation Given information :The given expression is sin 7 π 6 − sin π 3 Putting the direct value of cosine function. sin 7 π 6 − sin π 3 = − 1 2 − 3 2 = − ( 1 + 3 ) 2

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosi…

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Question

Chapter 5.4, Problem 8E

To determine

To find:To find the exact value of the expression sin(7π6−π3) .

Expert Solution

Answer to Problem 8E

The final answer is sin(7π6−π3)=12

Explanation of Solution

Given information:The given expression is sin(7π6−π3)

Using sum and difference formula sin(A−B)=sinA.cosB−cosA.sinB

We have

sin(7π6−π3)=sin(7π6).cos(π3)−cos(7π6).sin(π3)=−12.12+32.32=−14+34=12

To determine

To find:To find the exact value of the expression sin7π6−sinπ3 .

Expert Solution

Answer to Problem 8E

The final answer is sin7π6−sinπ3=−(1+3)2

Explanation of Solution

Given information:The given expression is sin7π6−sinπ3

Putting the direct value of cosine function.

sin7π6−sinπ3=−12−32=−(1+3)2

Chapter 5.4, Problem 7E

Chapter 5.4, Problem 9E

Chapter 5 Solutions

EBK PRECALCULUS W/LIMITS

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