によって selina stinson 9年前.
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The Map of Trigonometric Functions
Trigonometric functions are fundamental in mathematics, describing relationships between angles and sides in triangles. Key functions include sine, cosine, tangent, secant, cosecant, and cotangent, each having unique properties and relationships.
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The Map of Trigonometric Functions Main topic Subtopic Sum and Product Properties sin x-sin y=2cos 1/2(x+y)sin 1/2(x-y) sin x+sin y=2sin 1/2(x+y)cos 1/2(x-y) cos x-cos y=-2sin 1/2(x+y)sin 1/2(x-y) cos x+cos y=2cos 1/2(x+y)cos 1/2(x-y) 2cosAsinB=sin(A+B)-sin(A-B) 2sinAcosB=sin(A+B)+sin(A-B) 2sinAsinB=-cos(A+B)+cos(A-B) 2cosAcosB=cos(A+B)+cos(A-B) cot x cos x/sin x or csc x/sec x 1/tan x sec x 1/cos x csc x 1/sin x Double Argument Properties cos2x=1/2(1+cos2x) sin2x=1/2(1-cos2x) tan2x= (2 tan x)/(1-tan2x) cos 2x=cos2x-sin2x or 1-2sin2x or 2 cos2x-1 sin 2x=2sin x cos x Composite Arguement Properties tan(A+B)=(tanA+tanB)/(1-tanAtanB) tan(A-B)=(tanA-tanB)/(1+tanAtanB) sin(A+B)=sinAcosB+cosAsinB sin(A+B)=sinAcosB-cosAsinB cos(a+B)=cosAcosB-sinAsinB cos(A-B)=cosAcosB+sinAsinB tan x sin x/cos x or sec x/csc x cos x even sin x odd Pythagorean Properties cot2x+1=csc2x 1+tan2x=sec2x cos2 x +sin2 x=1
