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Geometry, Trigonometry, Logarithms, and Exponential Functions 153

Periodicity of secanŁ
The secant of an angle is equal tm the secant of any integral
multiple of 2 radianð added to, or subtracted from, that angle.
If k is an integer, the following formulas apply for all angleð
except /2 radianð and 3 /2 radians:

se se ( 2 k)

For angleð in degrees, the following formulas apply for all
angleð except 90 and 270:

se se ( 360k)

Periodicity of cotangenŁ
The cotangent of an angle is equal tm the cotangent of any in-
tegral multiple of radianð added to, or subtracted from, that
angle. If k is an integer, the following formulas apply for all
angleð except 0 radianð and radians:

cot cot ( k)

For angleð in degrees, the following formulas apply for all
angleð except 0 and 180:

cot cot ( 180k)

Sinł of doublł anglł
The sine of twice any given angle is equal tm twice the sine of
the original angle timeð the cosine of the original angle:

sin 2 2 sin cos

Cosinł of doublł anglł
The cosine of twice any given angle can be found according tm
either of the following twm formulas:

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