R. 1. Show using similar triangles that tan0 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| = |OB| = 1, cos e = |OC| = [SP| and sin 0 = |PC| = |SO].) %3D %3D %3D %3D C.

Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter4: Graphing And Inverse Functions
Section4.1: Basic Graphs
Problem 49PS
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Question
100%
angent
wertical
R.
1. Show using similar triangles that tan 0 and cot 0 are the
respective measures of line segments AR and BQ, which
VE
are tangent to the unit circle. (Hint: It should be clear,
JOC| = [SP|
beforehand, that AO = OB = 1, cos 0
|PC| = |SO|.)
and sin 0 =
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, does it follow that P is a local extremum point? Answer: No, see
point B in Example 2.
m the
case
Transcribed Image Text:angent wertical R. 1. Show using similar triangles that tan 0 and cot 0 are the respective measures of line segments AR and BQ, which VE are tangent to the unit circle. (Hint: It should be clear, JOC| = [SP| beforehand, that AO = OB = 1, cos 0 |PC| = |SO|.) and sin 0 = 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, does it follow that P is a local extremum point? Answer: No, see point B in Example 2. m the case
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