2sin60 sinA sin 120 A how to launch sin A 30 1

This is a proof question, and you start with the result you want to prove.

sin(a+30)=sinacos30+cosasin30= (root number3) 2 *sina + (1 2)*cosa

Original: 2sin60 = sina + sin(120-a) 2sin60 = root number 3

sin(120-a) = sin120cosa-cos120sina = (root number 3) 2 *cosa + (1 2) * sina

Root number 3 = (3 2) sina + (root number 3) 2 * cosa

Both sides of the equation are divided by : root number 3

This gives 1= (root number 3) 2 *sina + (1 2)*cosa

And thus it was proven. Can you read it? I don't know how to type, so I can only write like this, I hope you can understand it, and ask if you don't understand.

I don't know if you're in high school (the root number can't be written down).

Left 1 Right sina half of the root of three times the cosa -1 2sina1 2sina half of the root three times the cosasin (a+30')

Left Right.

Method 1: Define using trigonometric functions.

Let the angle a be an acute angle, at any point of its terminal edge p(m,n), then r= m 2+n 2sina = m r, cosa=n r, tana=m n (丌 + a) and the terminal edge of a is symmetrical with respect to the origin, then (丌 + a) the terminal point q and p are symmetrical with respect to the origin point, the coordinates are (-m, -n), r1= (-m) 2+(-n) 2=r

sin(丌+a)=-m r=-sina,cos(丌+a)=-n r=-cosa

tan(丌+a)=-m (-n)=tana Method 2: Use the same angle of the unit circle and the terminal edge, see the figure below

The first induction formula sin(180°+a)=-sina, explaining that 180=2*90° is unchanged as sin, as a is an acute angle, the third quadrant of a+180° position, its sine is less than 0, which is negative, and the second is according to the sum angle formula sin(180°+a)=sin180cosa+cos180sina=0*cosa+(-1)*sina=-sina

No matter how big the angle a is, treat it as an acute angle, 180 degrees minus the acute angle is equal to the second quadrant angle, and the sine is positive in the first and second quadrants, so sina = sin(180-a).

3 sin150 = sina sin(30-a) to get sina sin(30-a) = 2 3

sina=2√3sin(30-a)

sina = 2 sell noisy waiter 3 (1 2 * cosa- 3 2 * sina) sina= 3 cosa-3 sina

4sina = Li Xi 3cosa

tana=√3/4

No matter how big the angle a is, take it as an acute angle, 180 degrees minus the acute angle is equal to the angle of the second sliding simple quadrant, and the sine in the first and second quadrants is a positive and missing number, so sina=sin(180-a).

sin(-a)=-sina right? Wrong. - Vuten A is in the second quadrant, and the sine value is positive, i.e., sin(- a)=sina

sina+sin(150°-a)

2sin((a+150-a)/2)cos((a-150+a)/2)2sin75°cos(a-75°)

Root No. 2 + Root No. 6) 2*cos(a-75°)sina + sin(150°-a) range is [-(root empty grip No. 2 + root No. 6) 2,(root No. 2 + root No. 6) 2].

In this way, can you fight Xingqing with a bridge?

Harmony and difference Ji Gonghui quarrel formula: sin +sin =2sin[( chaotic sedan 2]cos[( former attendant 2] sina + sin(120°-a) =2sin[(a+120-a) 2]cos[(a-120+a) 2]=2sin60cos(a-60)=2sin60cos(a-60)=1cos(a+30-90)=sin(a+30)=1

According to the sin ( sin cos sin sin

sin(60-a)=sin60*cosa－cos60*sina

It is easy to calculate according to the triangular argument of the stove bend.