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(a) Apply the Mean Value Theorem to tan over [0, 0], where 0 < 0 < π/2. Hence show that tan 0 > 0 when 0 < 0 < π/2. [₁ (c) By combining your answers from parts (a) and (b), show that tan 0 > 0 + 0³/3, when 0 < 0 < π/2. (b) By writing tan² in terms of sec², show that tan²0 de = tan 0-0 + c.

(a) Apply the Mean Value Theorem to tan over [0, 0], where 0 < 0 < π/2. Hence show that tan 0 > 0 when 0 < 0 < π/2. [₁ (c) By combining your answers from parts (a) and (b), show that tan 0 > 0 + 0³/3, when 0 < 0 < π/2. (b) By writing tan² in terms of sec², show that tan²0 de = tan 0-0 + c.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.3: Trigonometric Functions Of Real Numbers
Problem 49E
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(a) Apply the Mean Value Theorem to tan over [0, 0], where 0 < 0 < π/2. Hence show that tan 0 > 0 when 0 < 0 < π/2. iftar (c) By combining your answers from parts (a) and (b), show that tan 0 > 0 + 0³/3, when 0 < 0 < π/2. (b) By writing tan² in terms of sec², show that tan²0 de - tan 0 - 0 + c.
Transcribed Image Text:(a) Apply the Mean Value Theorem to tan over [0, 0], where 0 < 0 < π/2. Hence show that tan 0 > 0 when 0 < 0 < π/2. iftar (c) By combining your answers from parts (a) and (b), show that tan 0 > 0 + 0³/3, when 0 < 0 < π/2. (b) By writing tan² in terms of sec², show that tan²0 de - tan 0 - 0 + c.
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