**Title:** Trigonometric Functions and Quadrants**Incorrect Attempt:**Your previous answers were incorrect for the following:- \( \sin 2x \): Your answer is incorrect.- \( \cos 2x \): Your answer is incorrect.- \( \tan 2x \): Your answer is incorrect.**Problem Statement:**Find \( \sin 2x \), \( \cos 2x \), and \( \tan 2x \) if \( \sin x = -\frac{2}{\sqrt{13}} \) and \( x \) terminates in quadrant III.**Solution Area:**```\sin 2x = \square\cos 2x = \square\tan 2x = \square```**Additional Information:**The user is instructed to solve for \( \sin 2x \), \( \cos 2x \), and \( \tan 2x \) using the given information and fill in the blanks. This problem requires knowledge of trigonometric identities and understanding of quadrant characteristics.**Hints:**- Recall the double angle identities: - \( \sin 2x = 2 \sin x \cos x \) - \( \cos 2x = \cos^2 x - \sin^2 x \) - \( \tan 2x = \frac{2 \tan x}{1 - \tan^2 x} \)- Since \( x \) is in quadrant III, the cosine and tangent of \( x \) will be negative.**Instructions:**Use the provided identities and the given value of \( \sin x \) to solve for the unknown trigonometric functions.© 2020 McGraw-Hill Education. All Rights Reserved. Terms of Use | Privacy | Accessibility**Note:** A small user interface with options for numerical input or functions is shown but not detailed.**Further Practice:** After solving, check your solutions by reflecting on the properties of trigonometric functions in different quadrants.

Name: **Title:** Trigonometric Functions and Quadrants**Incorrect Attempt:*
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: **Title:** Trigonometric Functions and Quadrants**Incorrect Attempt:**Your previous answers were incorrect for the following:- \( \sin 2x \): Your answer is incorrect.- \( \cos 2x \): Your answer is incorrect.- \( \tan 2x \): Your answer is incorrec