TrigFormulae - Various Trigonometric Equations You Will be...

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Unformatted text preview: Various Trigonometric Equations You Will be Expected to Know (1Z04 – Test #1) Basic Relations from the Definitions: csc(ϑ ) = 1 sin(ϑ ) tan(ϑ ) = sec(ϑ ) = sin(ϑ ) cos(ϑ ) 1 cos(ϑ ) cot(ϑ ) = cot(ϑ ) = 1 tan(ϑ ) cos(ϑ ) 1 = sin(ϑ ) tan(ϑ ) Pythagorean Relations: cos 2 (ϑ ) + sin 2 (ϑ ) = 1 1 + tan 2 (ϑ ) = sec2 (ϑ ) Double Angle Formulae: cos(2ϑ ) = cos 2 (ϑ ) − sin 2 (ϑ ) = 2 cos 2 (ϑ ) − 1 = 1 − 2sin 2 (ϑ ) sin(2ϑ ) = 2 cos(ϑ ) sin(ϑ ) Half-Angle Formulae (easily derivable from the double angle formula for cosine): cos 2 (ϑ / 2) = 1 (1 + cos(ϑ )) 2 sin 2 (ϑ / 2) = 1 (1 − cos(ϑ )) 2 Basic Derivative Formulae: d d cos(ϑ ) = − sin(ϑ ) sin(ϑ ) = cos(ϑ ) dx dx d d tan(ϑ ) = sec2 (ϑ ) sec(ϑ ) = sec(ϑ ) tan(ϑ ) dx dx Derivatives of Inverse Trigonometric Functions: d cos − 1 ( x ) = − dx 1 1− x 2 d sin − 1 ( x) = dx 1 1− x 2 d 1 tan − 1 ( x) = dx 1 + x2 Hyperbolic Functions: cosh( x ) = e x + e− x 2 sinh( x) = e x − e− x 2 tanh( x) = sinh( x ) cosh( x) sech( x) = 1 cosh( x) csch( x) = 1 sinh( x) coth( x) = 1 tanh( x) Hyperbolic Analogues to the Pythagorean Relations: cosh 2 ( x) − sinh 2 ( x) = 1 1 − tanh 2 ( x) = sech 2 ( x) Basic Hyperbolic Derivative Formulae: d cosh( x) = sinh( x) dx d sinh( x) = cosh( x) dx d tanh( x) = sech 2 ( x) dx ...
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TrigFormulae - Various Trigonometric Equations You Will be...

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