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For a right triangle with an angle θ : Sine Function: sin (θ) = Opposite / Hypotenuse. Cosine Function: cos (θ) = Adjacent / Hypotenuse. Tangent Function: tan (θ) = Opposite / Adjacent. When we divide Sine by Cosine we get: So we can say: That is our first Trigonometric Identity.
sinx cosx secx= 1 cosx cosecx= 1 sinx cotx= 1 tanx Fundamental trig identity (cosx)2 +(sinx)2 = 1 1+(tanx)2 = (secx)2 (cotx)2 +1 = (cosecx)2 Odd and even properties cos( x) = cos(x) sin( x) = sin(x) tan( x) = tan(x) Double angle formulas sin(2x) = 2sinxcosx cos(2x) = (cosx)2 (sinx)2 cos(2x) = 2(cosx)2 1 cos(2x) = 1 2(sinx)2 Half angle formulas ...
TRIGONOMETRY LAWS AND IDENTITIES DEFINITIONS Opposite Hypotenuse sin(x)= csc(x)= Hypotenuse 2Opposite 2 Adjacent Hypotenuse cos(x)= sec(x)= Hypotenuse Adjacent
C3 TRIGONOMETRY Worksheet D 1 a Write down the identities for sin (A + B) and cos (A + B). b Use these identities to obtain similar identities for sin (A − B) and cos (A − B). c Use the above identities to obtain similar identities for tan (A + B) and tan (A − B). 2 Express each of the following in the form sin α, where α is acute.
Printable & Online Trigonometry Worksheets. There are three reciprocal trigonometric functions, making a total of six including cosine, sine, and tangent. The reciprocal cosine function is secant: secθ = 1/cosθ. The reciprocal sine function is cosecant, cscθ = 1/sinθ.
The basic trigonometric identities are: Cosec θ = 1/Sin θ Sec θ = 1/Cos θ Cot θ = 1/Tan θ Tan θ = Sin θ/Cos θ Cot θ = Cos θ/Sin θ Sin2θ + Cos2 θ = 1 1 + tan 2 θ = sec 2 θ
sin2 +cos2 = 1 tan 2 +1 = sec 2 (This is just sin +cos 2 = 1 divided through by cos ) 1+cot 2 = csc 2 (This is just sin +cos 2 = 1 divided through by sin 2 )
