Sincosine theorem basic formula, sine cosine theorem formula, thank you

a sina=b sinb=c sinc=2rUses:1) Knowing the two corners of a triangle and one side, solve the triangle.

2) Knowing the two sides of the triangle and the angle of one of the sides, solve the triangle.

3) Use a:b:c=sina:sinb:sinc to solve the transformation relationship between angles.

Right-angled triangle.

An acute angle of the opposite side with an hypotenuse.

The ratio is called the sine of this angle.

1. Sinusoidal theorem: a sina=b sinb=c sinc=2r2, cos theorem: cos a=(b +c -a) 2bc.

The sine and cosine theorem refers to the sine theorem and the cosine theorem, which is an important theorem to reveal the relationship between the corners of triangles, and it can be used directly to solve the problem of triangles.

The ratio of the adjacent edge of an acute angle to the hypotenuse of a right triangle is called the cosine of the acute angle.

Trigonometric Formula:

Acute angle trigonometric formula.

sin = the opposite side of the hypotenuse.

cos = the adjacent edge of the hypotenuse.

tan = adjacent edge of the opposite edge.

cot = the opposite edge of the adjacent edge.

Doubling Angle Formula. sin2a=2sina•cosa

cos2a=cosa^2-sina^2=1-2sina^2=2cosa^2-1

tan2a=(2tana) (1-tana 2) (Note: sina 2 is the square sin2(a) of sina) induction formula.

sin(-α= -sinα

cos(-α= cosα

tan (—a)=-tanα

sin(π/2-α)= cosα

cos(π/2-α)= sinα

sin(π/2+α)= cosα

cos(π/2+α)= -sinα

sin(π-= sinα

cos(π-= -cosα

sin(π+= -sinα

cos(π+= -cosα

tana= sina/cosa

tan（π/2＋α）cotα

tan（π/2－α）cotα

tan（π－tanα

tan（π＋tanα

Induce formulas to memorize the trick: odd and even unchanged, and the symbol looks at the quadrant.

Magna formula. sin =2tan( 2) 1+tan ( 2) cos = 1-tan ( 2) 1+tan ( 2) tan =2tan( 2) 1-tan ( 2) Other formulas.

1)(sin ) 2+(cos) 2=1(2)1+(tan ) 2=(sec ) 2(3)1+(cot ) 2=(csc) 2 proves the following two formulas, just divide one formula by (sin ) 2, and divide the second by (cos) 2.

4) For any non-right triangle, there is.

tana+tanb+tanc=tanatanbtanc

Sine theorem and cosine theorem:

The sine theorem is a fundamental theorem in trigonometry, which states that "in any plane triangle, the ratio of the sinusoids of each side to the opposite angle is equal and equal to the diameter of the circumscribed circle", i.e., a sina = b sinb = c sinc = 2r = d (r is the radius of the circumscribed circle and d is the diameter).

The cosine theorem is a mathematical theorem describing the relationship between the length of three sides in a triangle and the cosine value of an angle, and is a generalization of the Pythagorean theorem in the general triangle and pants belt shape, and the Pythagorean theorem is a special case of the cosine theorem.

One or two discriminant methods of the cosine determination theorem:

If we remember that m(c1, c2) is the number of positive roots, the value of the plus sign before the root sign in the expression of c1 is c, and the value of the minus sign before the root sign in the expression c2 is the expression of c.

If m(c1,c2)=2, then there are two solutions.

If m(c1,c2)=1, then there is a solution.

If m(c1,c2)=0, then there is a zero solution (i.e., no solution before the destruction of purity).

Note: If C1 is equal to C2 and C1 or C2 is greater than 0, this situation is counted to the second case, that is, a solution.