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Unformatted text preview: " SOHCAHTOA ", i.e., sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent, Another mnemonic probably more common in Great Britain than the United States is "Tommy On A Ship Of His Caught A Herring." From the Pythagorean theorem , It is therefore also true that and The trigonometric functions can be defined algebraically in terms of complex exponentials (i.e., using the Euler formula ) as z Hybrid trigonometric product/sum formulas are Osborn's rule gives a prescription for converting trigonometric identities to analogous identities for hyperbolic functions . For imaginary arguments, For complex arguments, For the absolute square of complex arguments , The complex modulus also satisfies the curious identity The only functions satisfying identities of this form, are , , and...
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- Spring '11