can someone help Use a trig identities to find the following value exactly.sin(-105°)

Name: can someone help Use a trig identities to find the following value exa
Uploaded: 2024-03-20T07:07:37.000Z
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Description: can someone help Use a trig identities to find the following value exactly.sin(-105°)

We know that, sin-θ=-sinθ ⋯⋯1sin90°+θ=cosθ ⋯⋯2 We have, sin-105° By using the…

Answered: Use a trig identities to find the…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Analytic Trigonometry

Section: Chapter Questions

Problem 19T

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can someone help

Use a trig identities to find the following value exactly.
sin(-105°)

Expert Solution

Step 1

We know that,

$\begin{array}{rcl} \sin (- θ) & = & - \sin θ \dots \dots (1) \\ \sin (90 ° + θ) & = & \cos θ \dots \dots (2) \end{array}$

We have,

$\sin (- 105 °)$

By using the trigonometric identities given by equation (1) and (2), we get the result as

$\begin{array}{rcl} \sin (- 105 °) & = & - \sin (105 °) \\ = & - \sin (90 ° + 15 °) \\ = & - \cos (15 °) \end{array}$

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