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