-ANGULAR REFERENCES-


-as of [26 SEPTEMBER 2026]-


.


*3 DIMENSIONS* —>


-THE [STERADIAN]-


.


*2 DIMENSIONS* —>


-THE [RADIAN]-


-THE [DEGREE]-


.


[2π] radians = [360°]


[π] radians = [180°]


[1] radian = [57.2957°]


[1°] = [0.01745] radians


.


-[π]-


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-TO CONVERT “DEGREES” TO “RADIANS”, MULTIPLE THE [DEGREE VALUE] BY [π / 180]-


[π / 180] ≈ 0.01745


.


-TO CONVERT “RADIANS” TO “DEGREES”, MULTIPLE THE [RADIAN VALUE] BY [180 / π]-


[180 / π] ≈ 57.29578


.


*DEGREE SYMBOL* —>


°


*to type “degree symbol” on macOS* —>


-[SHIFT] + [OPTION] + [ 8 ]-


.


(there is no symbol for “radians”)


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*ANGLES* —>


-10 ANGLES-


(as of [27 SEPTEMBER 2026])


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*minimum* —>


-[0°]-


-HORIZON-



-STRAIGHT LINE-


.


-[6°]-


-CIVIL DAWN/DUSK-



.


-[12°]-


-NAUTICAL DAWN/DUSK-



.


-[18°]-


-ASTRONOMICAL DAWN/DUSK-



.


-[38.157°]-


-[0.666]-


(POSTERBOARD HORIZONTAL ACUTE ANGLE)


.


-[45°]-


-[π / 4]-


(~0.7854)


.


-[51.843°]-


-[0.905]-


(POSTERBOARD VERTICAL ACUTE ANGLE)


.


-[90°]-


-[π / 2]-


(~1.5708)


.


-[135°]-


-[3π / 4]-


(~2.3562)


.


-[180°]-


π


(~3.1416)


.


-[225°]-


-[5π / 4]-


(~3.92699)


.


-[270°]-


-[3π / 2]-


(~4.7124)


.


-[315°]–


-[7π / 4]-


(~5.4978)


.


*maximum* —>


-[360°]-


2π


(~6.2832)


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-as of [14 OCTOBER 2026]-

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*👨‍🔬🕵️‍♀️🙇‍♀️*SKETCHES*🙇‍♂️👩‍🔬🕵️‍♂️*

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👈👈👈☜*-FRAMING DIMENSIONS-* ☞ 👉👉👉

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*🌈✨ *TABLE OF CONTENTS* ✨🌷*

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🔥🔥🔥🔥🔥🔥*we won the war* 🔥🔥🔥🔥🔥🔥