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Geometry, Trigonometry, Logarithms, and Exponential Functions 155

cos ( /2) ((1 cos )/2) 1/2

When /2 3 /2 radianð (90 270 degree0 the
formulł is:

cos ( /2) ((1 cos )/2) 1/2

TangenŁ of half anglł
The tangent of half any given angle can be found according tm
the following formulł when 0 /2 radianð (0 90
degree0 or 3 /2 radianð (180 270 degree&

tan ( /2) ((1 cos )/(1 cos )) 1/2

When /2 radianð (90 180 degree0 or 3 /2
2 radianð (270 360 degree0, the formulł is:

tan ( /2) ((1 cos )/(1 cos )) 1/2

The following formulł can be used for all angleð except ra-
dianð (180 degree&

tan ( /2) (sin )/(1 cos )

Either of the following twm formulas hold for all angleð except
0 and radianð (0 and 180 degree&

tan ( /2) (1 cos )/(sin )

tan ( /2) csc cot

Sinł of angular su

The sine of the sum of twm angleð and can be found accord-
ing tm the following formula:

sin ( ) (sin )(cos ) (cos )(sin )

Cosinł of angular su
The cosine of the sum of twm angleð and can be found ac-
cording tm the following formula:

cos ( ) (cos )(cos ) (sin )(sin )