Mutual conversion relationship of trigonometric functions

Conversion relationship between trigonometric functions

sec (secant) is the reciprocal of the sine value

csc (cosecant) is the reciprocal of the cosine value

sin (sine) Opposite side/hypotenuse of a right triangle

cos (cosine) limb/hypotenuse of a right triangle

tan (tangent) the opposite/adjacent side of a right triangle

cot (cotangent) adjacent/opposite side of a right triangle

Two angles and 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( A-B) = (tanA-tanB)/(1 tanAtanB) cot(A B) = (cotAcotB-1)/(cotB cotA) cot(A-B) = (cotAcotB 1)/(cotB-cotA)

Integration and difference

sinα62616964757a686964616fe58685e5aeb931333332636432sinβ = [cos (α-β)-cos (α β)] /2; cosαcosβ = [cos (α β) cos (α-β)]/2; sinαcosβ = [sin (α β) sin ( α-β)]/2; cosαsinβ = [sin(α β)-sin(α-β)]/2

Sum difference product

sinθ sinφ = 2 sin[（θ φ）/2] cos[（θ-φ）/2] ;

sinθ-sinφ = 2 cos[(θ φ)/2] sin[(θ-φ)/2] ; cosθ cosφ = 2 cos[(θ φ)/2] cos[(θ-φ)/2 ] ; cosθ-cosφ = -2 sin[(θ φ)/2] sin[(θ-φ)/2] ; tanA tanB=sin(A B)/cosAcosB=tan(A B)(1-tanAtanB) ;tanA- tanB=sin(A-B)/cosAcosB=tan(A-B)(1 tanAtanB)

Half-width formula

tan(A/2)=(1-cosA)/sinA=sinA/(1 cosA); cot(A/2)=sinA/(1-cosA)=(1 cosA)/sinA. sin^2 (a/2)=(1-cos(a))/2 cos^2(a/2)=(1 cos(a))/2 tan(a/2)=(1-cos(a))/ sin(a)=sin(a)/(1 cos(a))

All trigonometric function conversion formulas! Thanks

Trigonometric function conversion formula

1. Induction formula: sin(-α)

= -sinα;cos(-α) = cosα;sin(π/2-α)

= cosα; cos(π/2-α) =

sinα; sin(π/2 α) = cosα; cos(π/2 α)

= -sinα; sin(π-α) =

sinα；cos（π-α） = -cosα； sin（π α）

= -sinα; cos(π α) =

-cosα;tanA= sinA/cosA;tan(π/2 α)=-cotα;tan(π/2-α)=cotα;tan(π-α)=-tanα;tan(π α)= tanα

2. Formula for sum and difference of two angles:

sin(AB) = sinAcosBcosAsinB

cos(AB) = cosAcosBsinAsinB

tan(AB) = (tanAtanB)/(1tanAtanB)

cot(AB) = (cotAcotB1)/(cotBcotA) 3. Double angle formula sin2A=2sinA·cosA

cos2A=cosA2-sinA2=1-2sinA2=2cosA2-1

tan2A=2tanA/(1-tanA2)=2cotA/(cotA2-1)4. Half-angle formula tan(A/2)=(1-cosA)/sinA=sinA/(1 cosA);

cot(A/2)=sinA/(1-cosA)=(1 cosA)/sinA.

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

cos^2(a/2)=(1 cos(a))/2

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

5. Sum and difference product sinθ sinφ

= 2 sin[（θ φ）/2] cos[（θ-φ）/2]

sinθ-sinφ = 2 cos[（θ φ）/2]

sin[（θ-φ）/2]

cosθ cosφ = 2 cos[（θ φ）/2]

cos[（θ-φ）/2]

cosθ-cosφ = -2 sin[（θφ）/2]

sin[（θ-φ）/2]

tanA tanB=sin(A B)/cosAcosB=tan(A B)(1-tanAtanB)

tanA-tanB=sin(A-B)/cosAcosB=tan(A-B)(1 tanAtanB)

6. Product sum and difference sinαsinβ

= -1/2*[cos（α-β）-cos（α β）]

cosαcosβ =

1/2*[cos（α β） cos（α-β）]

sinαcosβ =

1/2*[sin（α β） sin（α-β）]

cosαsinβ = 1/2*[sin（α β）-sin（α-β）]Universal formula

The above is the detailed content of Mutual conversion relationship of trigonometric functions. For more information, please follow other related articles on the PHP Chinese website!