Question is attached (8)Find the exact value of cos(tan-1(14/3)) by sketching the appropriate right triangle.

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Description: Question is attached (8)Find the exact value of cos(tan-1(14/3)) by sketching the appropriate right triangle.

Answered: (8) Find the exact value of…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter7: Analytic Trigonometry

Section: Chapter Questions

Problem 80RE

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Question is attached

(8)
Find the exact value of cos(tan-1(14/3)) by sketching the appropriate right triangle.

Expert Solution

Step 1

Given,

cos(tan^-1(14/3)) = ?

Step 2

Now

Let's assume

x = tan^-1(14/3)

then

tanx = 14/3 = Perpendicular / base

then assuming the perpendicular of right angle = 14k

and the base of the right angle = 3k where k is any constant

Now applying the Pythagoras theorem

(Hypotenuse)² = (Perpendicular)² + (base)²

= (14k)² + (3k)²

= 196 k² + 9k²

= 205k²

So, the Hypotenuse = $\sqrt{205}$ k

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