List of trigonometric identities

List of trigonometric identities - List of tr ig onometr ic...

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12/7/13 List of trigonometric identities - Wikipedia, the free encyclopedia en.wikipedia.org/wiki/List_of_trigonometric_identities 1/12 Notation [ edit ] Angles [ edit ] This article uses Greek letters such as alpha ( α ), beta ( β ), gamma ( γ ), and theta ( θ ) to represent angles . Several different units of angle measure are widely used, including degrees , radians , and grads : 1 full circle = 360 degrees = 2 radians = 400 grads. The following table shows the conversions for some common angles: Degrees 30° 60° 120° 150° 210° 240° 300° 330° Radians Grads 33⅓ grad 66⅔ grad 133⅓ grad 166⅔ grad 233⅓ grad 266⅔ grad 333⅓ grad 366⅔ grad Degrees 45° 90° 135° 180° 225° 270° 315° 360° Radians Grads 50 grad 100 grad 150 grad 200 grad 250 grad 300 grad 350 grad 400 grad Unless otherwise specified, all angles in this article are assumed to be in radians, but angles ending in a degree symbol (°) are in degrees. Per Niven's theorem multiples of 30° are the only rational angles with rational sin/cos, which may account for their popularity in examples. [1] Trigonometric functions [ edit ] The primary trigonometric functions are the sine and cosine of an angle. These are sometimes abbreviated sin( θ ) and cos( θ ), respectively, where θ is the angle, but the parentheses around the angle are often omitted, e.g., sin θ and cos θ . The tangent (tan) of an angle is the ratio of the sine to the cosine: Finally, the reciprocal functions secant (sec), cosecant (csc), and cotangent (cot) are the reciprocals of the cosine, sine, and tangent: These definitions are sometimes referred to as ratio identities . Inverse functions [ edit ] Main article: Inverse trigonometric functions The inverse trigonometric functions are partial inverse functions for the trigonometric functions. For example, the inverse function for the sine, known as the inverse sine (sin −1 ) or arcsine (arcsin or asin), satisfies and This article uses the notation below for inverse trigonometric functions: Function sin cos tan sec csc cot Inverse arcsin arccos arctan arcsec arccsc arccot Pythagorean identity [ edit ] The basic relationship between the sine and the cosine is the Pythagorean trigonometric identity : where cos 2 θ means (cos( θ )) 2 and sin 2 θ means (sin( θ )) 2 . This can be viewed as a version of the Pythagorean theorem , and follows from the equation x 2 + y 2 = 1 for the unit circle . This equation can be solved for either the sine or the cosine: Related identities [ edit ] Dividing the Pythagorean identity through by either cos 2 θ or sin 2 θ yields two other identities: Using these identities together with the ratio identities, it is possible to express any trigonometric function in terms of any other ( up to a plus or minus sign): Each trigonometric function in terms of the other five. [2] in terms of
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12/7/13 List of trigonometric identities - Wikipedia, the free encyclopedia en.wikipedia.org/wiki/List_of_trigonometric_identities 2/12 All of the trigonometric functions of an angle θ can be constructed geometrically in terms of a unit circle centered at O . Many of these terms are no longer in common use.
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List of trigonometric identities - List of tr ig onometr ic...

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