angentverticalR.1. Show using similar triangles that tan 0 and cot 0 are therespective measures of line segments AR and BQ, whichare tangent to the unit circle. (Hint: It should be clear,beforehand, that |AO|and sin 0 = |PC| = |SO|.)VE= |OB| = 1, cos 0 = |OC| = |SP|%3D%3D%3D%3D%3D2. We have seen that for a smooth graph, the tangent lines at the stationary points arealways horizontal. Ask the class if the converse is true, that is, if the tangent line at apoint P is horizontal, docs it follow that P is a local extremum point? Answer: No, seepoint B in Example 2.m thecase

Using figure ,∠QOA + ∠QOB = 90°⇒θ+∠QOB = 90°⇒∠QOB = 90°-θIn ∆QBO ,∠QBO = 90° and ∠QOB=90°-θ ⇒∠OQB =…

1. Show using similar triangles that tan 0 and cot 0 are the respective measures of line segments AR and BQ, which are tangent to the unit circle. (Hint: It should be clear, beforehand, that A0| = |OB| = 1, cos 0 = |OC| = [SP| %3D %3D and sin 0 = PC| = |S0|.) %3D

1. Show using similar triangles that tan 0 and cot 0 are the respective measures of line segments AR and BQ, which are tangent to the unit circle. (Hint: It should be clear, beforehand, that A0| = |OB| = 1, cos 0 = |OC| = [SP| %3D %3D and sin 0 = PC| = |S0|.) %3D

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 59E

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Question

angent
vertical
R.
1. Show using similar triangles that tan 0 and cot 0 are the
respective measures of line segments AR and BQ, which
are tangent to the unit circle. (Hint: It should be clear,
beforehand, that |AO|
and sin 0 = |PC| = |SO|.)
VE
= |OB| = 1, cos 0 = |OC| = |SP|
%3D
%3D
%3D
%3D
%3D
2. We have seen that for a smooth graph, the tangent lines at the stationary points are
always horizontal. Ask the class if the converse is true, that is, if the tangent line at a
point P is horizontal, docs it follow that P is a local extremum point? Answer: No, see
point B in Example 2.
m the
case

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