Two-angle sum formula?
Sin (A+B)? =? sinAcosB+cosAsinB?
Sin (A-B)? =? sinAcosB-cosAsinB?
cos(A+B)? =? cosAcosB-sinAsinB?
cos(A-B)? =? cosAcosB+sinAsinB?
Tan (A+B)? =? (tanA+tanB)/( 1-tanAtanB)?
Tan ()? =? (tanA-tanB)/( 1+tanAtanB)?
cot(A+B)? =? (cotAcotB- 1)/(cotB+cotA)?
Kurt (A-B)? =? (cotAcotB+ 1)/(cotB-cotA)?
Double angle formula?
tan2A? =? 2tanA/( 1-tan^2? a)?
Sin2A=2SinA? CosA?
Cos2A? =? Cos^2? Sin^2? Answer?
=2Cos^2? A— 1?
= 1—2sin^2? Answer?
Triple angle formula?
sin3A? =? 3sina-4(sina)^3; ?
cos3A? =? 4(cosA)^3? -3cosA?
tan3a? =? Tan? Answer? tan(π/3+a)tan(π/3-a)?
Half angle formula?
Sin (A/2)? =? √{( 1 - cosA)/2}?
cos(A/2)? =? √{( 1+cosA)/2}?
Tan (one/two)? =? √{( 1-cosA)/( 1+cosA)}?
cot(A/2)? =? √{( 1+cosA)/( 1-cosA)}?
Tan (one/two)? =? (1-cosA)/ Sina = Sina /( 1+cosA)?
Sum-difference product
Sin (a)+ sin (b)? =? 2sin[(a+b)/2]cos[(a-b)/2]?
Sin (1)-Sin (2)? =? 2cos[(a+b)/2]sin[(a-b)/2]?
cos(a)+cos(b)? =? 2cos[(a+b)/2]cos[(a-b)/2]?
cos(a)-cos(b)? =? -2sin[(a+b)/2]sin[(a-b)/2]?
tanA+tanB=sin(A+B)/cosAcosB?
Product and difference?
Crime (a) and crime (b)? =? - 1/2*[cos(a+b)-cos(a-b)]?
cos(a)cos(b)? =? 1/2*[cos(a+b)+cos(a-b)]?
sin(a)cos(b)? =? 1/2*[sin(a+b)+sin(a-b)]?
Cos(a) crime (b)? =? 1/2*[sin(a+b)-sin(a-b)]?
Inductive formula?
Sin (-a)? =? -sin (1)?
cos(-a)? =? cos(a)?
sin(π/2-a)? =? cos(a)?
cos(π/2-a)? =? Crime (1)?
sin(π/2+a)? =? cos(a)?
cos(π/2+a)? =? -sin (1)?
sin(π-a)? =? Crime (1)?
cos(π-a)? =? -cos(a)?
sin(π+a)? =? -sin (1)?
cos(π+a)? =? -cos(a)?
tgA=tanA? =? Sina /cosA?
Universal formula?
Crime (1)? =? [2tan(a/2)]? /? { 1+[tan(a/2)]^2}?
cos(a)? =? { 1-[tan(a/2)]^2}? /? { 1+[tan(a/2)]^2}?
Tan (1)? =? [2tan(a/2)]/{ 1-[tan(a/2)]^2}?
Other recipes?
Answer? Sin (a)+b? cos(a)? =? [√(a^2+b^2)]*sin(a+c]? [where tan(c)=b/a]?
Answer? Crime (A)-B? cos(a)? =? [√(a^2+b^2)]*cos(a-c]? [where tan(c)=a/b]?
1+sin(a)? =? 【sin(a/2)+cos(a/2)]^2; ?
1-sin(a)? =? 【sin(a/2)-cos(a/2)]^2; ; ?
Other non-critical trigonometric functions?
csc(a)? =? 1/sin(a)?
sec(a)? =? 1/cos(a)?
Hyperbolic function?
Singh (a)? =? [e^a-e^(-a)]/2?
cosh(a)? =? [e^a+e^(-a)]/2?
tg? h(a)? =? Sin? h(a)/cos? h(a)?
Formula 1:?
Let α be an arbitrary angle, and the values of the same trigonometric function with the same angle of the terminal edge are equal:?
sin(2kπ+α)=? sinα?
cos(2kπ+α)=? cosα?
tan(2kπ+α)=? tanα?
cot(2kπ+α)=? cotα?
Formula 2:?
Let α be an arbitrary angle. What is the relationship between the trigonometric function value of π+α and that of α?
sin(π+α)=? -Xin α?
cos(π+α)=? -cosα?
tan(π+α)=? tanα?
cot(π+α)=? cotα?
Formula 3:?
Arbitrary angle α sum? The relationship between trigonometric function values of-α:?
sin(-α)=? -Xin α?
cos(-α)=? cosα?
tan(-α)=? -tanα?
cot(-α)=? -cotα?
Formula 4:?
The relationship between π-α and the trigonometric function value of α can be obtained by Formula 2 and Formula 3:?
sin(π-α)=? sinα?
cos(π-α)=? -cosα?
tan(π-α)=? -tanα?
cot(π-α)=? -cotα?
Formula 5:?
Using formula-and formula 3, we can get the trigonometric function value of 2π-α and α:?
sin(2π-α)=? -Xin α?
cos(2π-α)=? cosα?
tan(2π-α)=? -tanα?
cot(2π-α)=? -cotα?
Equation 6:?
The relationship between π/2 α and 3 π/2 α and the trigonometric function value of α:?
sin(π/2+α)=? cosα?
cos(π/2+α)=? -sinα