Explanation Given: ► Assume that π ≤ θ < 3 π 2 ► tan θ = 4 . Trigonometry is a branch of mathematics that focuses on relationships between the sides and angles of triangles. In trigonometry there are trigonometric ratios that relate the angle measures of a right triangle to the length of its sides. The six trigonometric functions for any right angled triangle by assuming that the angle θ lies between 0 to π 2 (in radians) are defined as below. Trigonometric Functions Table: Description: For considering the right angled triangle A B C sin θ = O p p o s i t e S i d e H y p o t e n u s e sin θ = A B A C sin θ = a h cos θ = Adjacent S i d e H y p o t e n u s e cos θ = B C A C cos θ = b h tan θ = O p p o s i t e S i d e A d j a c e n t S i d e tan θ = A B A C tan θ = a b csc θ = H y p o t e n u s e O p p o s i t e S i d e csc θ = A C A B csc θ = h a sec θ = H y p o t e n u s e O p p o s i t e S i d e sec θ = A C B C sec θ = h b cot θ = A d j a c e n t S i d e O p p o s i t e S i d e cot θ = A C A B cot θ = b a Signs of Trigonometric Functions: Quadrant In Degrees In Radians sin θ cos θ tan θ csc θ = 1 sin θ sec θ = 1 cos θ cot θ = 1 tan θ I 0 ∘ t o 90 ∘ 0 t o π 2 + v e + v e + v e + v e + v e + v e I I 90 ∘ t o 180 ∘ π 2 t o π + v e − v e − v e + v e − v e − v e I I I 180 ∘ t o 270 ∘ π t o 3 π 2 − v e − v e + v e <

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.

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Question

Chapter 1.4, Problem 26E

To determine

The values of cosθ and sinθ if tanθ=4, by assuming that π≤θ<3π2

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Chapter 1.4, Problem 25E

Chapter 1.4, Problem 27E

Chapter 1 Solutions

Calculus - Standalone book

Ch. 1.1 - Prob. 1PQ Ch. 1.1 - Prob. 2PQ Ch. 1.1 - Prob. 3PQ Ch. 1.1 - Prob. 4PQ Ch. 1.1 - Prob. 5PQ Ch. 1.1 - Prob. 6PQ Ch. 1.1 - Prob. 7PQ Ch. 1.1 - Prob. 8PQ Ch. 1.1 - Prob. 9PQ Ch. 1.1 - Prob. 10PQ

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