Trigonometric functions induce formula problems TAT 30

tan(π-=2

So tan = -2

Original = 2sin( +cos( 2+ )sin(3 2+)sin

2sin²а-cosаsinа

2sin²а／sin²а-cosаsinа／sin²а2-tanа

So the answer is 4

The induction formula trigonometric function is as follows:

Basic formulas for trigonometric functions:

1. Equation 1: The relationship between the arbitrary angle and the trigonometric value of the eggplant-: sin( sin cos( cos tan( tan cot( cot

2. Formula 2: sin( +sin cos( +cos tan( +tan cot( +cot

3. Equation 3: Using Equation 2 and Equation 3, we can obtain the relationship between - and the value of the slip function of the three tremors: sin( sin cos( cos tan( tan cot( cot

4. Equation 4: The relationship between the trigonometric values of 2 - and by using Equation 1 and Equation 3: sin(2 sin cos(2 cos tan(2 tan cot(2 cot

5. Equation 5: The relationship between the trigonometric values of 2 and : sin(2+)cos cos(2+)sin tan(2+)cot cot(2+)tan sin(2)cos cos(2)sin tan(2)cot cot(2)tan.

is to derive the + formula first.

Then derive - the formula. In the Cartesian coordinate system, + and are symmetrical with respect to point o, it is easy to find the symmetry point p1(x1,y1) of a point p(x,y) on their terminal edge and the relationship between r and r1, and then according to the definition of trigonometric function, we get the example sin( +sin

Wait a minute. And use this set of formulas to derive - formulas: such as sin( -sin( +sin(- sin)=sin, etc.

Regarding the induction formula, all the formulas can be summarized as: odd and even unchanged, and the sign looks at the quadrant.

Odd and even unchanged:

That is, to see whether the coefficient before 2 is odd or even, if it is even, then the function name does not change, if it is odd, it becomes its supernumerical function.

sin(3 2+a), 3 is odd so it becomes cos, and cot( +a), 2* 2, 2 is even so it is unchanged, and the function name is still cot

Symbol look at quadrant:

That is, regardless of the size of a here, it is regarded as an acute angle.

Then look at the whole in parentheses in the quadrants, plus or minus.

For example, sin(3 2+a), a is regarded as an acute angle. Then (3 2+a) is in the fourth quadrant and sin(3 2+a) is negative.

So sin(3 2+a) = -cosa

For example, tan(+a-b) is also regarded as an acute angle, then (+a-b) is in the third quadrant, and tan(+a-b) is corrected.

So tan( +a-b) = tan(a-b).

Another example is cos(2-a), which also regards a as an acute angle, (2-a) is in the first quadrant, and cos(2-a) is correct.

So cos(2-a)=sina

I wrote it all by myself, including examples.

I was also a freshman in high school. Encourage you.

This is the mantra for memorizing trigonometric induction formulas. For example, calculate: sin240; tan240sin240=sin(180+60)=-sin60；

sin240=sin(270-30)=-cos30。

The above 180 degrees is an even (2) times 90 degrees, and the result is still the original function (sine), while 270 degrees is an odd (3) times 90 degrees, and the result becomes the cosine of the original function, because the original angle 240 degrees is the angle of the third limit, and the sign of the original function is negative.

"Odd and even unchanged" means that the degree in front of the angle is a multiple of 90 degrees. If it is an even number, the name of the function does not change, and if it is an odd number, it becomes its cofunction (positive and cosine change each other, positive and cotangent change each other, and forward and cosecant change each other).

"Symbol looking at quadrant" means that it is necessary to obey the sign of the original function in the quadrant where the original angle is located.

Hello, the trigonometric function induction formula you want is as follows, Formula 1: Let any angle, the value of the same trigonometric function of the same angle with the end edge is equal.

sin(2kπ+αsinα(k∈z)

cos(2kπ+αcosα(k∈z)

tan(2kπ+αtanα(k∈z)

cot(2kπ+αcotα(k∈z)

Equation 2: Set to any angle, the relationship between the trigonometric value of + and the trigonometric value of .

sin(π+sinα

cos(π+cosα

tan(π+tanα

cot(π+cotα

Equation 3: The relationship between the trigonometric value of an arbitrary angle and -.

sin(－αsinα

cos(－αcosα

tan(－αtanα

cot(－αcotα

Equation 4: Using Equation 2 and Equation 3, we can get the relationship between - and the trigonometric value of .

sin(π－sinα

cos(π－cosα

tan(π－tanα

cot(π－cotα

Equation 5: Using Equation 1 and Equation 3, we can get the relationship between the trigonometric values of 2 - and .

sin(2π－αsinα

cos(2π－αcosα

tan(2π－αtanα

cot(2π－αcotα

Equation 6: The relationship between the trigonometric values of 2 and .

sin(π/2+α)cosα

sin(π/2－α)cosα

cos(π/2+α)sinα

cos(π/2－α)sinα

tan(π/2+α)cotα

tan(π/2－α)cotα

cot(π/2+α)tanα

cot(π/2－α)tanα

Use the induction formula or the reverse induction formula to deform and achieve the desired formula.

f(x)=sin(2x+2π/3)

sin(2x+2π/3-2π)

sin(2x+3π/2-5π/6)

sin[(2x-5π/6)+3π/2]

cos(2x-5π/6)

cos[-(5π/6-2ⅹ)]

cos(5π/6-2x)。

Patchwork the identity deformation, with the aim of piecing together 5-6-2x, and then use the induced formula.

Take the sinusoidal function sina as an example, when it becomes sin( +a), because the coefficient is odd, so there may be a change between sin( +a) and sina , we can set the angle a is the angle of the first quadrant, then ( +a) is the angle of the third quadrant, and the sine function is negative in the third quadrant, so sin( +a)=-sina; When it becomes sin(2 +a), the coefficient is even, so sin(2 +a) = sina

The cosine function is the same, ( +a) in cos( +a) is the angle of the third quadrant, and the cosine function is in the .

The second and third quadrants are negative, so cos( +a)=-cosa Another example: sin( -a)=sina, because -a is the second quadrant angle cos( -a)=-cosa

k 2, k is odd before k, tangent becomes cotangent, sine becomes cosine, and vice versa;

Look at the quadrants of the brackets, where the quadrant is positive and positive, and negative is negative.

For example, sin( +2)=cos ; Since 2 is an odd multiple of , the function name should be changed to cos, and since + 2 is the angle of the second quadrant, and the sine of the second quadrant is positive, and the result is coa( ) and so on, this can be solved.

Sine, cosine, and tangent formulas for double angles.

sin2α＝2sinαcosα cos2α＝cos^2(α)sin^2(α)2cos^2(α)1＝1－2sin^2(α)tan2α＝2tanα/(1－tan^2(α)

The formulas for sine, cosine, and tangent of half angles.

sin^2(α/2)＝(1－cosα)/2 cos^2(α/2)＝(1＋cosα)/2 tan^2(α/2)＝(1－cosα)/1＋cosα) tan(α/2)=(1—cosα)/sinα=sinα/1+cosα

Magna 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))

The sine, cosine, and tangent formula for triple angles.

sin3α＝3sinα－4sin^3(α)cos3α＝4cos^3(α)3cosα tan3α＝(3tanα－tan^3(α)1－3tan^2(α)

The sum of the difference product formulas for trigonometric functions.

sinα＋sinβ＝2sin((α2) ·cos((α2) sinα－sinβ＝2cos((α2) ·sin((α2) cosα＋cosβ＝2cos((α2)·cos((α2) cosα－cosβ＝－2sin((α2)·sin((α2)

Formula for the product and difference of trigonometric functions.

sinα·cosβ＝

These are not induction formulas.,What you're looking for is the relationship between different life trigonometric functions.,Read the reference book yourself.,There's a lot.,But only a few.,It's useless to have more.,In addition,Steal posts.。

Don't be noisy upstairs).

sin²a+cos²a=1

tan²a+1=sec²a

cot²a+1=csc²a

tana*cota=1

sina*csca=1

cosa*seca=1

Hahahaha)