Explanation Given: ► Assume that 0 ≤ θ ≤ π 2 ► cos θ = 5 13 . 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

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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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 25E

To determine

The values of cosθ and tanθ if sinθ=0.4, by assuming that π2≤θ<π

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Chapter 1.4, Problem 24E

Chapter 1.4, Problem 26E

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Chapter 1 Solutions

CALCULUS (CLOTH)

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