Senior 1 Math Trigonometry Help, High School Math Trigonometry Problem Solving

sinx, cosx: x r; Range: y [-1,1], period 2 ;

The definition domain of tanx: x≠k -( 2), the value range: y (-period is cotx's definition domain: x≠k, the value range, period, and parity are the same as those of tanx;

sinx, tanx, and cotx are odd functions, and cosx is an even function.

You can combine the above images to memorize.

y=2sin(3x+ 4)-1 (graphing) defines the domain x r

-1 sin(3x+ 4) 1

3 2sin(3x+ 4)-1 1, i.e., the range of f(x): f(x) [3,1].

The minimum value of f(x) is -3 and the maximum value is 1;

sin3x is parity, but sin(3x+4) is not.

The period of sianx is: t=2

The period of f(x) is: t=2 =2 3

1) The domain of f(x) is defined as (-

2）f(x)=2sin(3x+π/4)=2sin(3(x+π/12))

Periodicity: 3x=2

x=2π/3

Note: The period of y=sinx is 2

3）f(-x)=2sin(3(-x)+π/4)=2sin(π/4-3x)≠-2sin(3x+π/4)=-f(x)

is non-odd and non-even.

Note: sinx is an odd function, cosx is an even function, but sinx+cosx is non-odd and non-even.

4) Maximum: 2

Description: y=asinx sinx [-1,1] has a maximum value

f（x）＝2sin（3x＋π／4）－1

2sin[3（x+π/12）] 1

3 means that the function image is scaled down horizontally by 1 3 --period t=2 3 , and after translating to the left by 12, the function changes from the original odd function to non-odd and non-even!

The value range has shifted from -2 to 2 downwards by 1, and has become -3 to 1 to figure out the most basic sine function image first

The definition range is the range of the value of the independent variable x, and by default it is all meaningful ranges, but in some problems it is only a part of it (the questioner will give a certain range according to the actual situation).

Parity means that if the image of a function is symmetric with respect to the y-axis, then the function is an even function f(-x)=f(x); If the image of a function is symmetrical with respect to the origin, then the function is an odd function f(-x) = -f(x).

Defining domain: r Parity: Non-odd non-even Periodicity: t=2 3

Maximum: y=2 x=k*2 3+12

Minimum: y=-2 x=k*2 3+5 12

The maximum value is the number before sin, and then add the number after that number. The maximum values here are 1 and -3

The method of parity is to look at the relationship between f(x) and f(-x), when f(x) = f(-x) is even, when -f(x) = f(-x) is odd, here is the even function.

Periodically use 2 divided by the number before x. That is, 2 3

I'll give you a way, parity is judged by f(-x).

Just substitute the expression.

f(-x)=2sin(-3x+4)-1 is non-odd and non-even.

The period is t=2 w......w=3

It's so simple, I don't even want to say it, plus, I'll help you again.

I don't know if there are any calculation errors in the 20 questions, so let's verify it yourself.

First, turn sin5 2x into sin( 2x+1 2x).

Progressively, using the doubling formula, it is finally reduced to f(x)=2(cosx)2 (where 2 is squared) + cosx-1

The second question is to obtain the minimum value at x=-1 4, which is -9 8

1.Let tan(8)=a, tan 4=2a(1-a2).

1=2a/(1-a^2)

a^2-12a=0

a = root number 2-1, or - root number 2-1, but - root number 2-1<-1, so tan( 8) = root number 2-1

The same steps can be used to find tan(12)=2-root number 3, cot(12)=2

The root number is 3, so tan(8).

cot(12) = root number 2-1

2 root number 3 = root number 2

Root number 31cos (4 7).

cos(6π/7)

cos(2π/7)

2cos^2(2π/7)-1

cos(4π/7)cos(2π/7)-sin(4π/7)sin(2π/7)

cos(2π/7)

2cos^2(2π/7)-1

2cos^2(2π/7)-1]cos(2π/7)-2sin(2π/7)cos(2π/7)sin(2π/7)

cos(2π/7)

2cos^2(2π/7)-1

2cos^3(2π/7)-cos(2π/7)-2sin^2(2π/7)cos(2π/7)

cos(2π/7)

2cos^2(2π/7)-1

2cos^3(2π/7)-cos(2π/7)-2[1-cos^2(2π/7)]cos(2π/7)

2cos^2(2π/7)-1

2cos^3(2π/7)-2cos(2π/7)

2cos^3(2π/7)

12cos^3(2π/7)

2cos^3(2π/7)

4cos^3(2π/7)-1

Trigonometric functions are flexible, mainly to observe the angle values, and find some special relationships from them, such as 10 and 20, half-angle relations, 20 and 70, each other is co-angles, these are enough. Oh, and the other thing is that if it's not a common angle, it has to be converted to the same angle before it can be calculated.

In general, memorize a few formulas:

1) Induction formulas, set too much, not listed one by one, such as sin( -a)=sina

2) The double angle formula, sin2a=2sina*cosacos2a=cos a-sin a=1-2sin a=2cos a-1

3) Magna Formula:

sin2a=2tana (1+tan a)cos2a=(1-tan a) (1+tan a)a means of treatment:

If known. tana, find (a*sina + b*cosa) (csina+dcosa), the numerator and denominator are divided by cosa

I turn into a formula about おお.

<> first investigation of the six questions of the report file and the defeat of friends.

<> such as the family model code calendar map Zhaochang.

∵ ∠aeb=2α，∠acb=α

eac=2α-α=α= ∠acb

EAC is an isosceles triangle.

ea=ec=900

adb=4α，∠aeb=2α

dae=4 -2 =2 = aeb dae is an isosceles triangle.

da=de=300√3

Do DM perpendicular to Ae in M

DAE is an isosceles triangle.

ma = me = ae/2 = 900/2 = 450∴ cos∠dea=me/de=450/(300√3) = √3/2∴ ∠dea = 30°

sin ∠dea = 1/2

Tower height ab = aesin dea = 450

The value range of x-6 is [- 6, 6].

sin(- 6)<0 and then sin0=0 to have zero 6 0