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Junior high school mathematics trigonometric function table
Trigonometric function is an important knowledge point in junior high school mathematics. Next, I sorted out the trigonometric function table of junior high school mathematics, hoping to be helpful to mathematics learning.

Mathematical special trigonometric function value

Application of trigonometric function in junior high school mathematics trigonometric function has a more important application in complex numbers. Trigonometric function is also a common tool in physics.

There are six basic functions: function names: sine, cosine, tangent, cotangent, secant and cotangent;

Symbols: sin, cos, tan, cot, sec, csc.

Sine function sin(A)=a/c

Cosine function cos(A)=b/c

Tangent function tan(A)=a/b

Cotangent function cot(A)=b/a

Where a is the opposite side, b is the adjacent side and c is the hypotenuse.

Formulas of trigonometric functions table product sum and difference formula

sinαcosβ=( 1/2)*[sin(α+β)+sin(α-β)]

cosαsinβ=( 1/2)*[sin(α+β)-sin(α-β)]

cosαcosβ=( 1/2)*[cos(α+β)+cos(α-β)]

sinαsinβ=-( 1/2)*[cos(α+β)-cos(α-β)]

Sum-difference product formula

sinα+sinβ= 2 sin[(α+β)/2]cos[(α-β)/2]

sinα-sinβ= 2cos[(α+β)/2]sin[(α-β)/2]

cosα+cosβ= 2cos[(α+β)/2]cos[(α-β)/2]

cosα-cosβ=-2 sin[(α+β)/2]sin[(α-β)/2]

Triple angle formula

sin3α=3sinα-4sin^3α;

cos3α=4cos^3α-3cosα

The trigonometric function relationship between the sum and difference of two angles

sin(α+β)=sinαcosβ+cosαsinβ

sin(α-β)=sinαcosβ-cosαsinβ

cos(α+β)=cosαcosβ-sinαsinβ

cos(α-β)=cosαcosβ+sinαsinβ

tan(α+β)=(tanα+tanβ)/( 1-tanαtanβ)

tan(α-β)=(tanα-tanβ)/( 1+tanαtanβ)

Sine double angle formula

sin2α=2cosαsinα

Deduction: SIN2A = SIN (a+a) = SINA COSA+COSA SINA = 2 SINA COSA.

Extended formula: sin2a = 2sinacosa = 2tanacosa = 2tana/[1+tan2a]

1+sin2A=(sinA+cosA)^2

Cosine double angle formula

The cosine double angle formula has three sets of expressions, which are equivalent:

1.Cos2a = Cos2a-Sin2a =[ 1-tan2a]/[ 1+tan2a]

2.Cos2a= 1-2Sin2a

3.Cos2a=2Cos2a- 1

Deduction: cos2a = cos (a+a) = cosacosa-sinasina = cos2a-sin2a = 2cos2a-1

= 1-2sin^2A

Tangent dihedral formula

tan2α=2tanα/[ 1-tan2α]

Deduction: tan2a = tan (a+a) = (tana+tana)/(1-tanatana) = 2tana/[1-tan2a]

Reduced power formula

cosA^2=[ 1+cos2A]/2

sinA^2=[ 1-cos2A]/2

tana^2=[ 1-cos2a]/[ 1+cos2a]

Variant: sin2α = sin2 (α+π/4)-cos2 (α+π/4) = 2sin2 (a+π/4)-1=1-2cos2 (α+π/4); cos2α=2sin(α+π/4)cos(α+π/4)

Cosine theorem:

a^2=b^2+c^2-2bc*cosA

b^2=c^2+a^2-2ca*cosB

c^2=a^2+b^2-2ab*cosC