Current location - Training Enrollment Network - Mathematics courses - When did you learn the auxiliary angle formula?
When did you learn the auxiliary angle formula?
Mathematics is the shortcoming of many people, so what is the auxiliary angle formula? How long have you studied? Interested friends come and have a look with me. The following is when did you learn the auxiliary angle formula, which I compiled for you, for reference only. Welcome to read.

When did you learn the auxiliary angle formula?

Auxiliary angle formula is the content of compulsory four in senior high school mathematics. The auxiliary angle formula is as follows:

1. Sum and difference formula of two angles (remember everything written)

sin(A+B)= Sina cosb+cosa sinb;

sin(A-B)= Sina cosb-sinBcosA;

cos(A+B)= cosa cosb-Sina sinb;

cos(A-B)= cosa cosb+Sina sinb;

tan(A+B)=(tanA+tanB)/( 1-tanA tanB);

tan(A-B)=(tanA-tanB)/( 1+tanA tanB).

2. With the above formula, the following double-angle formula can be derived.

tan2a=2tana/[ 1-(tana)^2];

cos2a=(cosa)^2-(sina)^2=2(cosa)^2 - 1= 1-2(sina)^2;

(The cosine above is very important)

sin2A=2sinA*cosA .

3. Half-angle ones just need to remember this.

tan(A/2)=( 1-cosA)/sinA = sinA/( 1+cosA)。

4. The power decreasing formula can be derived from the cosine of double angle.

(sina)^2=( 1-cos2a)/2;

(cosA)^2=( 1+cos2A)/2。

5. Using the power drop formula above, the following commonly used simplified formulas can be derived.

1-cosa=sin^(a/2)*2;

1-sinA=cos^(A/2)*2。

Further reading: What else is the formula of trigonometric function?

Acute angle formula of trigonometric function:

Opposite side/hypotenuse of sinα=∞α;

Adjacent side/hypotenuse of cosα=∞α;

Opposite side of tan α = adjacent side of ∠ α/∠α;

Adjacent side of cot α = opposite side of ∠ α/∠α.

Double angle formula:

Sin2A = 2SinACosA

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

tan2A=(2tanA)/( 1-tanA^2)。

(Note: Sina 2 is the square of Sina 2 (a))

Triple angle formula:

sin 3α= 4 sinαsin(π/3+α)sin(π/3-α);

cos 3α= 4 cosαcos(π/3+α)cos(π/3-α);

tan3a = tan a tan(π/3+a) tan(π/3-a).

Derivation of triple angle formula;

sin3a = sin(2a+a)= sin 2 acosa+cos 2 asina .

Power consumption reduction formula:

sin^2(α)=( 1-cos(2α))/2=versin(2α)/2;

cos^2(α)=( 1+cos(2α))/2=covers(2α)/2;

tan^2(α)=( 1-cos(2α))/( 1+cos(2α))。