### Trigonometric Function Calculation#### Problem Statement:If \( \tan t = -\frac{4}{3} \) and \( \frac{3\pi}{2} < t < 2\pi \), find \( \sin t \), \( \cos t \), \( \sec t \), \( \csc t \), and \( \cot t \).#### Instructions:Enter the exact answers.- \( \sin t = \)- \( \cos t = \)- \( \sec t = \)- \( \csc t = \)- \( \cot t = \)#### Explanation:You are given the tangent of an angle \( t \) and the range within which \( t \) lies. Based on this information, you need to determine the sine, cosine, secant, cosecant, and cotangent of \( t \). Remember to consider the quadrant in which the angle \( t \) lies to determine the signs of the trigonometric functions.To find the values:1. Use the identity \( \tan t = \frac{\sin t}{\cos t} \) to set up a relationship between \( \sin t \) and \( \cos t \).2. Use the Pythagorean identity \( \sin^2 t + \cos^2 t = 1 \) to solve for \( \sin t \) and \( \cos t \).3. Compute the other trigonometric functions using their respective definitions: - \( \sec t = \frac{1}{\cos t} \) - \( \csc t = \frac{1}{\sin t} \) - \( \cot t = \frac{1}{\tan t} \)Make sure all answers are in exact form, not decimal approximations.

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Answered: I 43 3π and < t < 2 π, find sint, cost,…

I 43 3π and < t < 2 π, find sint, cost, sect, csct, cott. If tan t = Enter the exact answers. sint = cost = sect = csc t = cott = = Al

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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