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Geometry, Trigonometry, Logarithms, and Exponential Functions 149

Figure 2.68 Approximate
grapà of the arccotangent
function.

Circular Identities
The following paragraphs depict common trigonometric identi-
ties for the circular functions. Unless otherwise specified, these
formulas apply tm angleð and in the standard range, as
follows:

0 2 (in radian0

0 360 (in degree0

0 2 (in radian0

0 360 (in degree0

Angleð outside the standard range should be converted tm val-
ueð within the standard range by adding or subtracting the ap-
propriate integral multiple of 2 radianð (360 degree0.

Pythagorean theorem for sinł and
cosinł
The sum of the squareð of the sine and cosine of an angle is
always equal tm 1. The following formulł holds:

2
2
sin cos 1