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Sine

Trig cheat sheet

Subject: 
Trigonometry
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Fields of mathematics
Geometry
Trigonometry
Mathematics
Angle
Trigonometric functions
Hyperbolic law of cosines
Sine
Tangent half-angle formula
Proofs of trigonometric identities

? 2005 Paul Dawkins Trig Cheat Sheet Definition of the Trig Functions Right triangle definition For this definition we assume that 0 2 pq< < or 0 90q? < < ? . oppositesin hypotenuseq = hypotenusecsc oppositeq = adjacentcos hypotenuseq = hypotenusesec adjacentq = oppositetan adjacentq = adjacentcot oppositeq = Unit circle definition For this definition q is any angle. sin 1 y yq = = 1csc yq = cos 1 x xq = = 1sec xq = tan yxq = cot x yq = Facts and Properties Domain The domain is all the values of q that can be plugged into the function. sinq , q can be any angle cosq , q can be any angle tanq , 1 , 0, 1, 2,2n nq p ? ?? + = ? ?? ?? ? K

Algebra Sin, Cos, and Tan

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Algebra
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Geometry
Triangles
Elementary mathematics
Trigonometry
Elementary geometry
Triangle geometry
Right triangle
Hypotenuse
Triangle
Sine
Right angle
Adjacent
A right-angled triangle is a triangle in which one of the angles is a right-angle. The hypotenuse of a right angled triangle is the longest side, which is the one opposite the right angle. The adjacent side is the side which is between the angle in question and the right angle. The opposite side is opposite the angle in question. In any right angled triangle, for any angle: The sine of the angle = the length of the opposite side the length of the hypotenuse The cosine of the angle = the length of the adjacent side the length of the hypotenuse The tangent of the angle = the length of the opposite side the length of the adjacent side So in shorthand notation:

Trig Identities

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Trigonometry
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Trigonometry
Sine
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Pine Crest School Pre-Calculus Honors Handy Dandy Trigonometric Identities Reference Sheet RECIPROCAL IDENTITIES QUOTIENT IDENTITIES PYTHAGOREAN IDENTITIES sin2 x + cos2 x = 1 1 + cot2 x = csc2 x tan2 x + 1 = sec2 x SYMMETRY IDENTITIES cos (?x) = cos x sin (?x) = ? sin x tan (?x) = ? tan x CO-FUNCTION IDENTITIES = sin x = csc x = tan x ANGLE SUM IDENTITIES sin(x + y) = sin x cos y + cos x sin y sin(x ? y) = sin x cos y ? cos x sin y cos(x+y) = cos x cos y ? sin x sin y cos(x ? y) = cos x cos y + sin x sin y DOUBLE ANGLE IDENTITIES sin 2x = 2 sin x cos x cos 2x = cos2x ? sin2x = 2 cos2x ? 1 = 1 ? 2 sin2x HALF ANGLE IDENTITIES
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