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Simple high school math problems (too many) get high marks.
one page

Example 3? ∵cos(π+α)=-cosα=- 1/2∴α=5π/3? sin(2π-α)=-sinα=√3/2

Example 4? sin(α-3π)=-sinα=2cosα? The original score is (sinα+5cosα)/(-2cosα+sinα)=-3/4.

Two pages

Example 1? ( 1)cos 225 =-cos 45 =-√2/2(2)sin( 1 1π/3)=? sin( 1 1π/3-4π)=-? sin(π/3)=-√3/2

(3)? sin(- 16π/3)=? sin(- 16π/3+6π)=? sin(2π/3)=? √3/2

(4)cos(-2040)= cos(-2040+6×360)= cos 120 =- 1/2

Example 2? sin(360 +α)=sinα? cos(α+ 180 )=-cosα? sin(- 180 -α)=sinα? cos(- 180 -α)=-cosα

Original formula = 1

Three pages

Example 2? (1)sinx monotonically decreases at (π/2, π), and sin (2π/3) >; Sine (4π/5)

(2)tanx increases monotonically at (π/2,3 π/2) and tan (2 π/3)

(3)x in (π/4,? π/2), 1 >; sinθ& gt; √2/2,cosθ& lt; √2/2,tanθ& gt; 1,cosθ& lt; sinθ& lt; tanθ

Four pages

Example 1? sin(2π-α)=-sinα? cos(π+α)=-cosαcos(π/2+α)=-sinαcos( 1 1π/2-α)=? -sinα

cos(π-α)=-cosπsin(π-α)=sinα? sin(-π-α)=sinαsin(9π/2+α)=cosα

Original formula =-tanα

Example 2 COS (π/4+α) = SIN (π/2-π/4-α) = SIN (π/4-α)? Original formula = 1

Example 3? sin(3π+θ)=-sinθ,sinθ= 1/3

The form of the fraction is:1(1+cos θ)+1(1-cos θ) = 2/(1-cos θ 2) = 2/sin θ 2 =18.

Example 4? By simplifying the known formula, sinα+cosα= 1/5 can be obtained.

(sinα+cosα)^2=? sinα^2+cosα^2+2sinαcosα= 1+2sinαcosα

sinαcosα=- 12/25

The decomposition of the cubic sum formula can be obtained: the original formula =(sinα+cosα) (? sinα^2+cosα^2-sinαcosα)=37/ 125

Five pages

Example 3? According to the p coordinate, sin α = y/√ (y 2+3) =? √2y/4

y =√5sinα=√ 10/4 tanα=-√ 15/3

y =-√5sinα=-√ 10/4 tanα=√ 15/3

Example 4 (1) x-π/4 ≠π/2+kπ (k = 0, 1, 2, 2 ...)

x≠3π/4+kπ(k=0, 1,2,2……)

(2)cosx≠0,x≠π/2+kπ(k=0, 1,2,2……)

Do six pages of calculations by yourself.

Seven pages

1? F(x)=sinx(-sinx)+sinxsinx=0 even function

2( 1)f(α)=-cosα

(2)sinα=- 1/5, α is three quadrant angle, COSA =-2 √ 6/5, and f (α) = 2 √ 6/5.

(3)f(α)=-cos- 1860 =-cos 60 =- 1/2

3? sinθ=- 1/4? The results of fractional simplification are the same as those in the previous pages. 2/sinθ 2 = 32。

4 let y=π/2-x, and the function is f (siny) = cos (17π/2-17y) = sin17y.

Eight pages

Example 5? tan(2π-α)=? tan(-α)=? tan(α)sin(-2π-α)=sin-α=-sinα? cos(6π-α)=cos-α=cosα

sin(α+3π/2)=-cosα? cos(α+3π/2)=sinα

You can get it by substituting the score: left =-tanα= right.

Example 6? Tan(2π/3-α)=-tan(α+π/3) can be known from the range of α.

sin(α+π/3)>0,? sin(α+π/3)=√( 1-m^2)tan(α+π/3)=? √( 1-m^2)/m

Nine pages

Example 5? f(2007)= asin(2007π+α)+bcos(2007π+β)=? -Octyl α-β-keto alcohol

f(2008)= asin(2008π+α)+bcos(2008π+β)=? asinα+bcosβ=-? f(2007)=-5

Example 6? cos(π/6-α)=-? cos(π/6-α-π)=-? cos(5π/6+α)

sin(α-π/6)^2= 1-? cos(π/6-α)^2=2/3

Original formula =-3/3-2/3

2? f(θ)=(cosθ^2+cosθ-2)/(2cosθ^2+cosθ+2)=5/ 12

3? Same as example 6 √ (1-m2)/m.

Ten pages

Example 3? ( 1)(2kπ-5π/6,2kπ-π/6)(2)? (2kπ-π/3,2kπ+π/3)(3)? (kπ+π/4,kπ+π)

(4)(? 2kπ-π/6,2kπ+π/3)∩(2kπ+2π/3,2kπ+7π/6)

(5)(? 2kπ-3π/4,2kπ+π/4)

Example 4? ∵x∈(0,? π/2)∴sinx>; 0,cosx & gt0

(sinx+cosx)^2=sinx^2+cosx^2+2sinxcosx= 1+2sinxcosx>; 1

sinx+cosx & gt; 0? ∴sinx+cosx=√((sinx+cosx)^2)=√( 1+2sinxcosx)>; 1

Variants 1 and 2 are both obtained on the unit circle (circle with radius of 1), and the angle is x, and x is also the arc length on the corresponding unit circle. Sinx is the length of the line segment where the intersection of the edge of this angle (not the X axis) and the circle makes X perpendicular to the X axis, and tanx is the length of the line segment where the tangent of the circle passes through the circle and the X axis and makes the circle intersect the edge of this angle. The following figure

sinx^2+cosx^2=ab^2/oa^2+ob^2/)a^2=(ab^2+ob^2)/oa^2= 1

sinx = AB/OA = AB & lt; AC< arc AC = x