Circle, trig values, arc length, sector, chord, segment

Radius r of circle:
Angle α in degrees:
OR
Angle α in radians:      0 π/6 π/4 π/3 π/2 2π/3 3π/4 5π/6 π

   

Circle: Circumference=      Area=
x = r cos α =      y = r sin α =
Arc length L=αr =      Sector area S=αr2/2 =   
Chord length c = r√2√(1-cos α ) =   Segment area=   Sagitta height= r-√(r2-(c/2)2) =

sin α csc α
cos α sec α
tan α cot α

Earth radius: 3959 mi, 6371 km

Degrees ° a Radians cos sin
0 0 1 0
30 π/6 ≈ .5235 √3/2≈.866 1/2=.5
45 π/4 ≈ .7853 √2/2≈.7071 √2/2≈.7071
60 π/3 ≈ 1.0471 1/2=.5 √3/2≈.866
90 π/2 ≈ 1.5707 0 1
120 2π/3 ≈ 2.0943 -1/2=-.5 √3/2≈.866
135 3π/4 ≈ 2.3561 -√2/2≈-.7071 √2/2≈.7071
150 5π/6 ≈ 2.6179 -√3/2≈-.866 1/2=.5
180 π ≈ 3.141592 -1 0
270 3π/2 ≈ 4.7123 0 -1

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