T R I 



To find the area of a spherical A. 

 Let A, B, C be the three angles, then 



Area - A + B + C 180. or, if r = radius of the sphere, area = 

 r X (A-f B 4-C 180). 



III. TRIGONOMETRICAL FORMULAE. 



1. If s sin. and c cos. of an arc A j the arcs, of which t is the sine* 

 are comprehended within the two formulae. 



2 n T + A, and (2 n + 1) x ~ A, where x =: ISO. 

 Do., of which s is the sine, are 



(2 n -f- 1) a- + A, and (2 n + 2) - A. 

 Do., of which c is the cosine, are 



2 n tr + A and (2 n -f 2) 3- A. 



Do., of which c is cosine, are 



(2 n + 1) jr A and (2 n -f 1) * + A 

 in all which cases n may be 0, 1, 2, 3, &c. 



2. Sin. (| + A) ^ sin. (| -A). 



3. Cos. A. = sin. ^ |- A ) = sin. f ~ 4. A ) . 



4. Sin. A. = cos. 



_ /I cos. 2 A 2 tan. | A 



^ " "~ 2i 



' cot. ^ A+ tan.| A cot. A-j- tan. 4 A' 



