Current location - Training Enrollment Network - Mathematics courses - What are the formulas for postgraduate mathematics?
What are the formulas for postgraduate mathematics?
Mathematics preparation for postgraduate entrance examination: sum and difference formula from two angles

1, formulas of trigonometric functions of 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)

2, double angle formula:

Sine, Cosine and Tangent Formulas of Double Angles (Ascending Power and Shrinking Angle Formula)

sin2α=2sinαcosα

cos2α=cos^2(α)-sin^2(α)=2cos^2(α)- 1= 1-2sin^2(α)

tan2α=2tanα/[ 1-tan^2(α)]

3. Half-angle formula:

Sine, cosine and tangent formulas of half angle (power decreasing and angle expanding formulas)

sin^2(α/2)=( 1-cosα)/2

cos^2(α/2)=( 1+cosα)/2

tan^2(α/2)=( 1-cosα)/( 1+cosα)

And tan (α/2) = (1-cos α)/sin α = sin α/(1+cos α).

4. General formula:

sinα=2tan(α/2)/[ 1+tan^2(α/2)]

cosα=[ 1-tan^2(α/2)]/[ 1+tan^2(α/2)]

tanα=2tan(α/2)/[ 1-tan^2(α/2)]

Derivation of general formula;

Attached derivation: sin 2 α = 2 sin α cos α = 2 sin α cos α/(cos 2 (α)+sin 2 (α)) ...

(because cos 2 (α)+sin 2 (α) = 1)

Divide the * fraction up and down by COS 2 (α) to get SIN 2 α = 2 tan α/( 1+tan 2 (α)).

Then replace α with α/2.

Similarly, the universal formula of cosine can be derived. By comparing sine and cosine, a general formula of tangent can be obtained.

5, triple angle formula:

Sine, cosine and tangent formulas of triple angle;

sin3α=3sinα-4sin^3(α)

cos3α=4cos^3(α)-3cosα

tan3α=[3tanα-tan^3(α)]/[ 1-3tan^2(α)]