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Trigonometry Definitions and Functions

Trigonometry Definitions and Functions

Find a Trigonometry Definition and Function Reference/Cheat Sheet (with formulas).
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Trig Definition Math Help

Right Triangle Def.
Sine Def.
Cosine Def.
Tangent Def.
Cosecant Def.
Secant Def.
Cotangent Def.
Unit Circle Def.
Properties of Trig Func.
Domain
Range
Period
Inverse Trig Func.
Def. of Inverse Trig Func.
Domain of Inverse Trig
Range of Inverse Trig


Trig Definition Math Help

Right Triangle Definition

To define the trigonometric functions of an angle theta assign one of the angles in a right triangle that value. The functions sine, cosine, and tangent can all be defined by using properties of a right triangle. A right triangle has one angle that is 90 degrees. The longest side of the triangle is the hypotenuse. The side opposite theta will be referred to as opposite. The other side next to theta will be referred to as adjacent. The following properties exist:

Sine Definition


latex!encoded:base64,c2luXHRoZXRhPVxmcmFje29wcG9zaXRlfXtoeXBvdGVudXNlfQ==


Cosine Definition


latex!encoded:base64,Y29zXHRoZXRhPVxmcmFje2FkamFjZW50fXtoeXBvdGVudXNlfQ==


Tangent Definition


latex!encoded:base64,dGFuXHRoZXRhPVxmcmFje29wcG9zaXRlfXthZGphY2VudH0=


Cosecant Definition


latex!encoded:base64,Y3NjXHRoZXRhPVxmcmFje2h5cG90ZW51c2V9e29wcG9zaXRlfQ==


Secant Definition


latex!encoded:base64,c2VjXHRoZXRhPVxmcmFje2h5cG90ZW51c2V9e2FkamFjZW50fQ==


Cotangent Definition


latex!encoded:base64,Y290XHRoZXRhID0gXGZyYWN7YWRqYWNlbnR9e29wcG9zaXRlfQ==



Unit Circle Definition


latex!encoded:base64,c2luXHRoZXRhID0geQ==


latex!encoded:base64,Y29zXHRoZXRhID0geA==


latex!encoded:base64,dGFuXHRoZXRhID0gXGZyYWN7eX17eH0=


latex!encoded:base64,Y3NjXHRoZXRhID0gXGZyYWN7MX17eX0=


latex!encoded:base64,c2VjXHRoZXRhID0gXGZyYWN7MX17eH0=


latex!encoded:base64,Y290XHRoZXRhID0gXGZyYWN7eH17eX0=



Properties of Trig Functions

Domain

The possible angle input for each function is defined below:


latex!encoded:base64,c2luXHRoZXRhIFwgLCBcdGhldGE= can be any angle


latex!encoded:base64,Y29zXHRoZXRhIFwgLCBcdGhldGE= can be any angle


latex!encoded:base64,dGFuXHRoZXRhLCBcdGhldGEgXG5lcSBcbGVmdCAoIG4gKyBcZnJhY3sxfXsyfSBccmlnaHQgKSBccGkgLCBuPTAsXHBtMSxccG0yLC4uLg==


latex!encoded:base64,Y3NjXHRoZXRhLCBcdGhldGEgXG5lcSBuXHBpLCBcIG49MCxccG0xLFxwbTIsLi4u


latex!encoded:base64,c2VjXHRoZXRhLCBcdGhldGEgXG5lcSBcbGVmdCAoIG4gKyBcZnJhY3sxfXsyfSBccmlnaHQgKSBccGkgLCBuPTAsXHBtMSxccG0yLC4uLg==


latex!encoded:base64,Y290XHRoZXRhLCBcdGhldGEgXG5lcSBuXHBpLCBcIG49MCxccG0xLFxwbTIsLi4u



Range

The ranges of values possible for each of these functions are:


latex!encoded:base64,LTFcbGVxIHNpblx0aGV0YVxsZXEx


latex!encoded:base64,LTFcbGVxIGNvc1x0aGV0YVxsZXEx


latex!encoded:base64,LVxpbmZ0eVxsZXEgdGFuXHRoZXRhXGxlcVxpbmZ0eQ==


latex!encoded:base64,Y3NjXHRoZXRhXGdlcSAxIFwgYW5kIFwgY3NjXHRoZXRhXGxlcS0x


latex!encoded:base64,c2VjXHRoZXRhXGdlcSAxIFwgYW5kIFwgc2VjXHRoZXRhXGxlcS0x


latex!encoded:base64,LVxpbmZ0eVxsZXEgY290IFx0aGV0YSBcbGVxIFxpbmZ0eQ==


Period

The periods for each of these trig functions are:


latex!encoded:base64,c2luKFxvbWVnYVx0aGV0YSkgXHRvIFQ9XGZyYWN7MlxwaX17XG9tZWdhIH0=


latex!encoded:base64,Y29zKFxvbWVnYVx0aGV0YSkgXHRvIFQ9XGZyYWN7MlxwaX17XG9tZWdhIH0=


latex!encoded:base64,dGFuKFxvbWVnYVx0aGV0YSkgXHRvIFQ9XGZyYWN7XHBpfXtcb21lZ2EgfQ==


latex!encoded:base64,Y3NjKFxvbWVnYVx0aGV0YSkgXHRvIFQ9XGZyYWN7MlxwaX17XG9tZWdhIH0=


latex!encoded:base64,c2VjKFxvbWVnYVx0aGV0YSkgXHRvIFQ9XGZyYWN7MlxwaX17XG9tZWdhIH0=


latex!encoded:base64,Y290KFxvbWVnYVx0aGV0YSkgXHRvIFQ9XGZyYWN7XHBpfXtcb21lZ2EgfQ==


Inverse Trig Functions

Definition of Inverse Trig Functions

The definitions of the inverse trig functions are:


latex!encoded:base64,eT1zaW5eey0xfXggIFwgXHRleHR1cHt3aGVyZX0gXCB4ID0gc2lueQ==


latex!encoded:base64,eT1jb3Neey0xfXggIFwgXHRleHR1cHt3aGVyZX0gXCB4ID0gY29zeQ==


latex!encoded:base64,eT10YW5eey0xfXggIFwgXHRleHR1cHt3aGVyZX0gXCB4ID0gdGFueQ==


Inverse Trig functions are also notated as:


latex!encoded:base64,c2luXnstMX14XGVxdWl2IGFyY3NpbnggXGVxdWl2IEFzaW54


latex!encoded:base64,Y29zXnstMX14XGVxdWl2IGFyY2Nvc3ggXGVxdWl2IEFjb3N4


latex!encoded:base64,dGFuXnstMX14XGVxdWl2IGFyY3RhbnggXGVxdWl2IEF0YW54


Domain of Inverse Trig Functions

latex!encoded:base64,c2luXnstMX14OiAtMSBcbGVxIHggXGxlcTE=


latex!encoded:base64,Y29zXnstMX14OiAtMSBcbGVxIHggXGxlcTE=


latex!encoded:base64,dGFuXnstMX14OiAtXGluZnR5IFxsZXEgeCBcbGVxXGluZnR5


Range of Inverse Trig Functions

latex!encoded:base64,c2luIFx0aGV0YSwgXHRoZXRh can be any angle


latex!encoded:base64,Y29zIFx0aGV0YSwgXHRoZXRh can be any angle


latex!encoded:base64,dGFuIFx0aGV0YSxcdGhldGEgXG5lIChuICtcZnJhY3sxfXsyfSkgXHBpLCBuID0gMCwgXHBtMSxccG0yLC4uLg==