# Trig Review - Construction Protocol

### Mike May, S.J. - 2/23/2006

This chart gives the step by step construction used above.

No. Name Definition
1 Point P0 Point at (0,2), circle shifted up for clarity
2 Circle UnitCircle Circle with center P0 and Radius 1
3 Point P Draggable Point on UnitCircle
4 Text Circle "Unit Circle Coordinates = (" + (x(P)) + "," + (y(P) - 2) + ")"
5 Point P1 Point at (0,2) + (1,0)
6 Angle θ Angle between P1, P0, P
7 Text θ "θ = " + θ
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8 Line L1 Line through P perpendicular to yAxis
9 Point P3 intersection point of L1, yAxis - P moved to y axis
10 Segment sinθ Segment[P3, P]
11 Text sin θ "sin θ = " + (y(P) - 2) -- Remeber the shift
12 Point Sθ (θ, y(P) - 2) -- Traceable sin point
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13 Line L2 Line through P perpendicular to xAxis
14 Line L3 Line through P0, P1 - x axis shifted up through P0
15 Point P4 intersection point of L2, L3
16 Segment cosθ Segment[P, P4]
17 Text cosθ "cos θ = " + (x(P))
18 Point Cθ (θ, x(P)) -- Traceable cos point
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19 Line L4 Tangent through P to UnitCircle
20 Point P5 intersection point of L4, L3 -- tangent-secant point
21 Segment secθ Segment[P0, P5]
22 Text sec θ "sec θ = " + (x(P5))
23 Segment tanθ Segment[P, P5]
24 Text tan θ "tan θ = " + ((y(P) - 2) / x(P))
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25 Point P6 intersection point of L4, yAxis -- cotangent-cosecant point
26 Segment cscθ Segment[P6, P0]
27 Text csc θ "csc θ = " + (y(P6) - 2)
28 Segment cotθ Segment[P, P6]
29 Text cot θ "cot θ = " + (x(P) / (y(P) - 2))
Created with GeoGebra