High School Math Double Angle Formula, High School Math Double Angle Formula Questions

High school mathematics double angle formula beam difference: sin2 = 2sin cos, double angle formula is a group of formulas commonly used in mathematical trigonometric functions, through some transformation relations of the trigonometric value of the angle to express the trigonometric value of its double angle 2, the double angle formula includes the sine double angle formula, the cosine double angle formula and the tangent double angle formula.

In calculations, erasers can be used to simplify calculations and reduce the number of trigonometric functions, and it is also widely used in engineering Jane's. The cosine double angle formula has three sets of representations, and the three sets of forms are equivalent: cos2 = 2cos2 -1, cos2 = 1 2sin2, cos2 = cos2 sin2.

Tangent double angle: tan2 = 2tan [1-(tan ) 2], tan(1 2* )sin ) 1+cos )=1-cos ) sina.

The high school math double angle formula is as follows:

High school math double angle formula: tan2a=2tana [1-(tana) ]cos2a=(cosa) -sina) =2(cosa) 1=1-2(sina) ; sin2a=2sina*cosa。

The double angle formula is a group of formulas commonly used in mathematical trigonometric functions, which expresses the trigonometric value of its double angle 2 through some transformation relations of the trigonometric value of the angle, and the double angle formula includes the sine double angle formula, the cosine double angle formula and the tangent double angle formula. It can be used to simplify the calculation formula and reduce the number of trigonometric functions in the calculation of wheel car rulers, and it is also widely used in engineering.

Further reading: High School Math Problem Solving:

Special value test: For general mathematical problems, in the process of solving the problem, we can specialize the problem, and use the principle that if the problem is not true in a special case, it is not true in the general situation, so as to achieve the purpose of removing the false and preserving the true.

The principle of extremity: the problem to be studied is analyzed to the extreme state, so that the causal relationship becomes more obvious, so as to achieve the purpose of quickly solving the problem. Extremity is mostly used in finding extreme values, value ranges, and analytic geometry, and many problems with cumbersome calculation steps and large amount of calculations can be solved instantaneously once the extremity is used to analyze.

Elimination method: Using the information provided by the known conditions and the selection branch, three erroneous Talagao cases are eliminated from the four options, so as to achieve the purpose of correct selection. This is a commonly used method, especially when the answer is a fixed value, or there is a range of values, it can be excluded by substituting special points for verification.

Combination of numbers and shapes: from the conditions of the question, to make a figure or image that meets the meaning of the topic, with the help of the intuitiveness of the figure or image, through simple reasoning or calculation, so as to get the answer. The advantage of combining numbers and shapes is that it is intuitive, and you can even use a measuring ruler to measure the results directly.

Recursive induction: a method of reasoning through the conditions of the question, looking for patterns, and thus inducting the correct answer.

Reasoning method: a method that uses mathematical reasoning, formulas, rules, definitions, and questions to obtain results through direct calculus reasoning.

High school mathematics double angle formula: tan2a=2tana [1-(tana)] type late cos2a=(cosa) -sina) =2(cosa) 1=1-2(sina) ; sin2a=2sina*cosa。

The double angle formula is a group of formulas commonly used in mathematical trigonometric functions, which expresses the trigonometric value of the double angle 2 through some transformation relations of the trigonometric function value of the angle, and the double angle formula includes the Bu You Li sine double angle formula, the cosine double angle formula and the tangent double angle male mill sail formula. It can be used to simplify the calculation formula and reduce the number of trigonometric functions in calculations, and it is also widely used in engineering.

Exploit. 2(cosu) 2 -1 = cos(2u)u= lost cherry 4 -x 2

2[cos(4-x2)] 2-1cos[2(4-x2)].

cos(π/2 -x)

Profit and empty sales with cos( 2 -u)=sinusinx

The formula for double angles: sin2x=2sinxcosxcos2x=(cosx) 2-(sinx) 2=2(cosx) 2-1=1-2(sinx) 2tan2x=2tanx [1-(tanx) 2] The sinusoidal function is positive in the first and second quadrants and negative in the third and fourth quadrants. The cosine function is positive in the first and fourth quadrants and negative in the second and third quadrants.

The tangent function is positive in the first and third quadrants and negative in the second and fourth quadrants. sin2x=2sinxcosxcos2x=(cosx) 2-(sinx) 2=2(cosx) 2-1=1-2(sinx) 2tan2x=2tanx [1-(tanx) 2]sin2x=2sinxcosx,cos2x=cos(squared)x-sin(bi open hand squared)xsin2a=2sina*cosa cos2a=2(cosa) 2 -1 =1-2(sina) 2 tan2a=2tana ( 1-(tana) 2 )

Sinusoidal double angle male hand suspicious:

sin2α =2cosαsinα

Derivation: sin2a=sin(a+a)=sinacosa+cosinaina=2sinacosa

Extended formula: sin2a=2sinacosa = 2tanacosa 2=2tana [1+tana 2] 1+sin2a=(sina + cosa) 2

Cosine double angle formula:

The formula for cosine double angle has three sets of representations, and three sets of forms are equivalent:

Derivation: cos2a=cos(a+a)=cosacosa-sinasina=(cosa) 2-(sina) 2=2(cosa) 2-1

1-2(sina)^2

Tangent double angle formula:

tan2α=2tanα/[1-(tanα)^2]

Derivation: tan2a = tan(a+a) = (tana + tana) (1-tanatana) = 2tana [1-(tana) 2].

Magna formula. Early bond cosa 2=[1+cos2a] 2

sina^2=[1-cos2a]/2

From the formula of +, let = , that is, the formula of 2.

The formula for the sum of two angles, a special case when the two angles are equal.

For example, sin(x+y)=sinxcosy+cosxsiny, when x=y, there is.

sin2x=2sinxcosx

The same can be said. cos2x=cos²x-sin²x

tan2x=2tanx/(1-tan²x)

Basic Formula:

sin( +=sin cos +cos sin cos( +=cos cos -sin sin tan( +=(tan +tan ) (1-tan tan ) double angle formula derivation:

sin2α=sin（α+

sinαcosα+cosαsinα

2sinαcosα

cos2α=cos（α+

cosαcosα-sinαsinα

cosαcosα-sinαsinα

cos²α-sin²α

From sin +cos = 1, obtained.

sin = 1-cos, or cos = 1-sin is substituted into the above formula.

cos2 =2cos1 or cos2 =1-2sin tan2 =tan( +

tanα+tanα）/（1-tanαtanα）=2tanα/（1-tan²α）

Double angle formula: sin2x=2sinxcosxcos2x=(cosx) 2-(sinx) 2=2(cosx) 2-1=1-2(sinx) 2tan2x=2tanx [1-(tanx) 2].

The sine function is positive in the first and second quadrants and negative in the third and fourth quadrants. The cosine function is positive in the first and fourth quadrants and negative in the second and third quadrants. The tangent function is positive in the first and third quadrants and negative in the second and fourth quadrants.

sin2x=2sinxcosxcos2x=(cosx) 2-(sinx) 2=2(cosx) 2-1=1-2(sinx) 2tan2x=2tanx [1-(tanx) 2]sin2x=2sinxcosx,cos2x=cos(squared)x-sin(squared)xsin2a=2sina*cosa cos2a=2(cosa) 2 -1 =1-2(sina) 2 tan2a=2tana ( 1-(tana) 2 )

Sine double angle formula:

sin2α = 2cosαsinα

Derivation: sin2a=sin(a+a)=sinacosa+cosinaina=2sinacosa

Extended formula: sin2a=2sinacosa = 2tanacosa 2=2tana [1+tana 2] 1+sin2a=(sina + cosa) 2

Cosine double angle formula:

The formula for cosine double angle has three sets of representations, and three sets of forms are equivalent:

Derivation: cos2a=cos(a+a)=cosacosa-sinasina=(cosa) 2-(sina) 2=2(cosa) 2-1

1-2(sina)^2

Tangent double angle formula:

tan2α=2tanα/[1-(tanα)^2]

Derivation: tan2a = tan(a+a) = (tana + tana) (1-tanatana) = 2tana [1-(tana) 2].

Magna formula. cosa^2=[1+cos2a]/2

sina^2=[1-cos2a]/2