Sine theorem: In any plane triangle, the ratio of the sine value of each side to its diagonal is equal to and equal to the diameter of the circumscribed circle, that is, a/sinA = b/sinB =c/sinC= 2r=D, where r is the radius of the circumscribed circle and d is the diameter.

Cosine Theorem: For any triangle, the square of any side is equal to the sum of the squares of the other two sides minus twice the product of the cosine of the angle between these two sides and them, that is, cos A=(b+c-a)/2bc.

Equidistant trigonometric function

(1) square relation:

sin^2(α)+cos^2(α)= 1

tan^2(α)+ 1=sec^2(α)

cot^2(α)+ 1=csc^2(α)

(2) the relationship between products:

sinα= tanα* cosαcosα= cotα* sinαtanα= sinα* secαcotα= cosα* csα

secα= tanα* CSCαcsα= secα* cotα

Extended data

First, the application of sine theorem:

1, two angles and one side of the triangle are known, and the triangle is solved.

2. Know the angles of two sides of a triangle and one of them, and solve the triangle.

3. Use A: B: C = Sina: Sinb: Sinc to solve the conversion relationship between angles.

Second, the application of cosine theorem:

1. When two sides of a triangle and their included angles are known, the opposite sides of the known angles can be found from the cosine theorem.

2. When the three sides of a triangle are known, the three internal angles of the triangle can be obtained by cosine theorem.

3. When the three sides of a triangle are known, the area of the triangle can be obtained by cosine theorem.

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