Trigonometrical Functions 



In the diagram let the angle SOC = a, subtending chord SR and 

 arc SR; let angle OSC = b and let the Altitude, Base and Hypothe- 

 nuse be represented by the letters A, B and H. Then in any R. A. 

 triangle, when OS Rad. = 1, 



Sine 



a SC 



Cosine a OC 



Tangent a TR 



Cotangent a DG 



Secant a OT 



Cosecant a OG 



Versine 



a CR 



Covers! ne a 



SF 



Exsecant a - ST 

 Coexsecant a = SG 



H = B -5- cos a = A -f- sin a = A -=- cos b = B sin b 

 B = H X cos a = A X cot a = H X sin b = A tan b 

 A == H x a = B X tan a = H X cos b = B x cot b 

 sin a = A -r- H = cos b = tan a X cos a 

 cos a = B -r- H = sin b = 1 *vers a 

 tan a = A -f- B = ro/ b = // a -f- <w a 

 fl>/ a = B -T- H = ta b = 1 -~ tan a 

 /<rr a = H -r- B = cosec b = 1 -f- / a 

 a = H -7- A = / b = 1 -r- sin a 

 a = (H B) -=- H = covers b 

 covers a = (H A) -r- H = <vers b 



ex sec a = (H B) -:- B = coexsec b 

 coexsec a = (H A) -5- A = r/w b 



Functions of a 1 Grade or 1 Random 



B = 99.98477 



B - 700 



B =-57.20996 



In the third example the values of H and B are nearly identical 

 with each other and with the numerical value of a radian. The angle 

 which subtends an arc that is equal in length to the radius, is known 

 as a radian. It is equal to 360 U -=- ITT = 57.29578. This is therefore 

 the numerical value of the radius of a circle in which one unit of 

 length, measured along the circumference, subtends 1. 



