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15. Use your identities for the following: sec(r)- 2V3 tan(x)< 0. Find sin(x) and cot(x) 3 а.

15. Use your identities for the following: sec(r)- 2V3 tan(x)< 0. Find sin(x) and cot(x) 3 а.

Trigonometry (11th Edition)
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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**Problem Statement:** b. Evaluate: \(1 + \cot^2(18^\circ) - \sec^2(72^\circ)\) **Explanation:** This problem requires the evaluation of a trigonometric expression involving the cotangent and secant functions. - \(\cot(18^\circ)\) refers to the cotangent of 18 degrees, which is the reciprocal of the tangent function. - \(\sec(72^\circ)\) refers to the secant of 72 degrees, which is the reciprocal of the cosine function. Use known trigonometric identities and values to simplify and evaluate the expression for its numerical result.
Transcribed Image Text:**Problem Statement:** b. Evaluate: \(1 + \cot^2(18^\circ) - \sec^2(72^\circ)\) **Explanation:** This problem requires the evaluation of a trigonometric expression involving the cotangent and secant functions. - \(\cot(18^\circ)\) refers to the cotangent of 18 degrees, which is the reciprocal of the tangent function. - \(\sec(72^\circ)\) refers to the secant of 72 degrees, which is the reciprocal of the cosine function. Use known trigonometric identities and values to simplify and evaluate the expression for its numerical result.
**Problem 15: Trigonometric Identities** Use your identities for the following: Given: \[ \sec(x) = \frac{2\sqrt{3}}{3}, \quad \tan(x) < 0. \] Find \(\sin(x)\) and \(\cot(x)\). --- Note: The problem involves using trigonometric identities to find the values of sine and cotangent, given the secant value and the tangent condition.
Transcribed Image Text:**Problem 15: Trigonometric Identities** Use your identities for the following: Given: \[ \sec(x) = \frac{2\sqrt{3}}{3}, \quad \tan(x) < 0. \] Find \(\sin(x)\) and \(\cot(x)\). --- Note: The problem involves using trigonometric identities to find the values of sine and cotangent, given the secant value and the tangent condition.
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