3 Product-to-sum identities 4 说明 1 Angle sum and difference identities sin(α+β)=sinαcosβ+cosαsinβ,sin(α−β)=sinαcosβ−cosαsinβ,cos(α+β)=cosαcosβ−sinαsinβ,cos(α−β)=cosαcosβ+sin...
Basic Identities: sin(x)=1csc(x)sin(x)=1csc(x) cos(x)=1sec(x)cos(x)=1sec(x) tan(x)=1cot(x)tan(x)=1cot(x) sec(x)=1cos(x)sec(x)=1cos(x) csc(x)=1sin(x)csc(x)=1sin(x) ...
sin2(θ)+cos2(θ)=1 1+cot2(θ)=csc2(θ) tan2(θ)+1=sec2(θ) The first one is the Pythagorean theorem on the unit circle. The other two are derived by dividing the first one by either sine or cosine. Sum and Difference Identities The sum and differen...
sin(A)cos(B) = (1/2)[sin(A + B) + sin(A – B)] Just a handful of the basic trigonometric formulae are included here. These fundamentals serve as the foundation for several more complex formulae and identities. You’ll be able to tackle a variety of trigonometric issues with ease...
Double Angle Trigonometric Identities If the angles are doubled, then the trigonometric identities for sin, cos and tan are: sin 2θ = 2 sinθ cosθ cos 2θ = cos2θ – sin2θ = 2 cos2θ – 1 = 1 – 2sin2θ tan 2θ = (2tanθ)/(1 – tan2θ) ...
sin(−θ) = −sin(θ) cos(−θ) = cos(θ) tan(−θ) = −tan(θ)Double Angle IdentitiesHalf Angle IdentitiesNote that "±" means it may be either one, depending on the value of θ/2Angle Sum and Difference Identities
The Trigonometric Identities we introduced the(Sines, Cosines and Tangents). We begin by reminding ourselves of the 2X + Cos2X = 1 In addition, there are relations called: Sin 2X = 2 Sin X Cos X Cos 2X = Cos2X - Sin2X Because SinX + CosX = 1, this last relation can also be ...
Pythagorean Identities (毕达哥拉斯恒等式): sin²θ+cos²θ=1 1+tan²θ= sec²θ 1+cot²θ= csc²θ Cofunction Identities (余函数恒等式): The value of a trigonometric function of θ is equal to the cofunction of the complement of θ. ...
The “big three” trigonometric identities are (1)sin2t+cos2t=1 (2)sin(A+B)=sinAcosB+cosAsinB (3)cos(A+B)=cosAcosB−sinAsinB Using these we can derive many other identities. Even if we commit the other useful identities to memory, these...
In most examples where you see power 2 (that is,2), it will involve using the identitysin2θ+ cos2θ= 1(or one of the other 2 formulas that we derived above). Using these suggestions, you can simplify and prove expressions involving trigonometric identities. ...