Reciprocal relationship:
Brown canvas bed? = 1
sin csc？ = 1
Cos seconds? = 1
Relationship between businesses:
Sin? /cos？ = Tan? = seconds? /csc？
Because? /sin? =cot？ =csc？ /sec?
Square relation:
sin^2(？ )+cos^2(？ )= 1
1+tan^2(？ )=sec^2(？ )
1+cot^2(？ )=csc^2(？ )
Two commonly used formulas under different conditions
sin^2(？ )+cos^2(？ )= 1
Tan? _cot？ = 1
Special formula
(Sina+sin? _ (Sina -sin? )=sin(a+？ )_sin(a-？ )
Proof: (Sina+sin? _ (Sina -sin? )=2 sin[(？ +a)/2] cos[(a-？ )/2] _2 cos[(？ +a)/2] Crime [(a-? )/2]
=sin(a+？ )_sin(a-？ )
slope formula
We usually refer to the ratio of the vertical height h to the horizontal height l of the half slope as the slope (also called the slope ratio), which is represented by the letter I,
That is, i=h/l, and the general form of slope is written as l: m, such as i= 1:5. If the included angle between the slope and the horizontal plane is recorded as
A (called inclination angle), then I = h/l = tan a.
Acute angle formula of trigonometric function
Sine: sin? The opposite side of the hypotenuse of =/
Cosine: cos? =
Tangent: Tan? The opposite side of = and the adjacent side of/
A cot? Adjacent side of =/opposite side of =
Double angle formula
sine
sin2A=2sinA？ Kosa
cosine
1.Cos2a=Cos^2(a)-Sin^2(a)
2.Cos2a= 1-2Sin^2(a)
3.Cos2a=2Cos^2(a)- 1
That is, cos2a = cos2 (a)-sin2 (a) = 2cos2 (a)-1=1-2sin2 (a)
tangent
tan2A=(2tanA)/( 1-tan^2(A))
Triple angle formula
sin3？ = 4sinsin(？ /3+? ) sin (? /3-? )
cos3？ =4coscos(？ /3+? )cos(？ /3-? )
tan3a = tan a？ Tan (? /3+a)？ Tan (? /3-a)
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))
Sum difference product
Sin? +sin? = 2 sin[(？ +? )/2] cos[(？ -? )/2]
Sin? Sin? = 2 cos[(？ +? ) /2] sin [(? -? )/2]
Because? +cos？ = 2 cos[(？ +? )/2] cos[(？ -? )/2]
Because? Because? = -2 sin[(？ +? ) /2] sin [(? -? )/2]
tanA+tanB = sin(A+B)/cosa cosb = tan(A+B)( 1-tanA tanB)
tanA-tanB = sin(A-B)/cosa cosb = tan(A-B)( 1+tanA tanB)
Two-angle sum formula
Tan (? +? ) = (Tan? +Tan? )/( 1-tan？ Tan? )
Tan (? -? ) = (Tan? Tan? ) /( 1+ Tan? Tan? )
cos(？ +? )=cos？ Because? Sin? Sin?
cos(？ -? )=cos？ Because? +sin? Sin?
Sin (? +? ) = sin? Because? +cos？ Sin?
Sin (? -? ) = sin? Because? Because? Sin?
Sum and difference of products
Sin? Sin? =-[cos(？ +? )-cos(？ -? )] /2
Because? Because? = [cos(？ +? )+cos(？ -? )]/2
Sin? Because? = [sin (? +? )+sin(？ -? )]/2
Because? Sin? = [sin (? +? )-sin (? -? )]/2
Formula 1:
Settings? For any angle, the values of the same trigonometric function with the same angle of the terminal edge are equal:
sin(2k？ +? ) = sin?
cos(2k？ +? )= cos？
Tan (2k? +? ) = Tan?
cot(2k？ +? )= cot？
Equation 2:
Settings? For any angle, +? What is the trigonometric function value of? The relationship between trigonometric function values is:
Sin (? +? ) =-sin?
cos(？ +? )= -cos？
Tan (? +? ) = Tan?
cot(？ +? )= cot？
Formula 3:
Any angle? Use-? The relationship between trigonometric function values is:
Sin (-? ) =-sin?
cos(-？ )= cos？
Tan (- ) =-Tan?
cot(-？ )= -cot？
Equation 4:
Can be obtained by Formula 2 and Formula 3? -? With what? The relationship between trigonometric function values is:
Sin (? -? ) = sin?
cos(？ -? )= -cos？
Tan (? -? ) =-Tan?
cot(？ -? )= -cot？
Formula 5:
Using formula-and formula 3, we can get 2? -? With what? The relationship between trigonometric function values is:
Sin (2? -? ) =-sin?
cos(2？ -? )= cos？
Tan (2? -? ) =-Tan?
cot(2？ -? )= -cot？
Equation 6:
? /2 and 3? /2 and? The relationship between trigonometric function values is:
Sin (? /2+? )= cos？
cos(？ /2+? ) =-sin?
Tan (? /2+? )= -cot？
cot(？ /2+? ) =-Tan?
Sin (? /2-? )= cos？
cos(？ /2-? ) = sin?
Tan (? /2-? )= cot？
cot(？ /2-? ) = Tan?
Sin (3? /2+? )= -cos？
cos(3？ /2+? ) = sin?
Tan (3? /2+? )= -cot？
cot(3？ /2+? ) =-Tan?
Sin (3? /2-? )= -cos？
cos(3？ /2-? ) =-sin?
Tan (3? /2-? )= cot？
cot(3？ /2-? ) = Tan?
(above k? z)
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