sin(-a)=-sin(a)

cos(-a)=cos(a)

sin(2π-a)=cos(a)

cos(2π-a)=sin(a)

sin(2π+a)=cos(a)

cos(2π+a)=-sin(a)

sin(π-a)=sin(a)

cos(π-a)=-cos(a)

sin(π+a)=-sin(a)

cos(π+a)=-cos(a)

tgA=tanA=sinAcosA

2. The trigonometric function of the sum and difference of two angles

sin(a+b)= sin(a)cos(b)+cos(α)sin(b)

cos(a+b)= cos(a)cos(b)-sin(a)sin(b)

sin(a-b)= sin(a)cos(b)-cos(a)sin(b)

cos(a-b)= cos(a)cos(b)+sin(a)sin(b)

tan(a+b)= tan(a)+tan(b) 1-tan(a)tan(b)

tan(a-b)= tan(a)-tan(b) 1+tan(a)tan(b)

3. Sum-difference product formula

sin(a)+sin(b)= 2s in(a+B2)cos(a-B2)

Crime (1)? sin(b)=2cos(a+b2)

cos(a)+cos(b)= 2cos(a+B2)cos(a-B2)

cos(a)-cos(b)=-2s in(a+B2)sin(a-B2)

4. Sum and difference formula of products (the above formula is obtained in reverse)

sin(a)sin(b)=- 12？ [cos(a+b)-cos(a-b)]

cos(a)cos(b)= 12？ [cos(a+b)+cos(a-b)]

sin(a)cos(b)= 12？ [sin(a+b)+sin(a-b)]

5. Double angle formula

sin(2a)=2sin(a)cos(a)

cos(2a)= cos 2(a)-sin 2(a)= 2cos 2(a)- 1 = 1-2 sin 2(a)

6. Half-angle formula

sin2(a2)= 1-cos(a)2

cos2(a2)= 1+cos(a)2

tan(a2)= 1-cos(a)sin(a)= Sina 1+cos(a)

7. General formula

sin(a)=2tan(a2) 1+tan2(a2)

cos(a)= 1-tan 2(a2) 1+tan 2(a2)

tan(a)=2tan(a2) 1-tan2(a2)

8. Other Formulas (Derived)

Answer? Sin (a)+b? Cos(a)=a2+b2sin(a+c) where tan(c)=ba.

Answer? Crime (A)-B? Cos(a)=a2+b2cos(a-c) where tan(c)=ab.

1+sin(a)=(sin(a2)+cos(a2))2

1-sin(a)=(sin(a2)-cos(a2))2

csc(a)= 1sin(a)

Seconds (a)= 1 cosine (a)