Explanation Given: ► 0 ≤ θ ≤ π 2 ► sin θ = 3 5 . 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 If a trigonometric function is given then two sides of the right angles triangle are known; thereby we can find the third side of the triangle by using Pythagoras theorem which states that h 2 = a 2 + b 2

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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Chapter 1.4, Problem 20E

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The values of sinθ and tanθ if sinθ=35, by assuming that 0≤θ≤π2

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Chapter 1.4, Problem 19E

Chapter 1.4, Problem 21E

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The values of sin θ and tan θ if sin θ = 3 5 , by assuming that 0 ≤ θ ≤ π 2

Solution Summary: The author explains that trigonometry is a branch of mathematics that focuses on relationships between the sides and angles of triangles.

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The values of sinθ and tanθ if sinθ=35, by assuming that 0≤θ≤π2

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Chapter 1 Solutions