4-4 / 13 △ 8 / 39 + 3 / 2

4-4 / 13 △ 8 / 39 + 3 / 2

Original formula = 4-4 / 13 * 39 / 8 + 3 / 2 = 4 - (4 / 13 * 39 / 8) + 3 / 2 = 4-3 / 2 + 3 / 2 = 4-3 = 1
Find sin80 - √ 3cos80-2sin20
sin80°-√3cos80°-2sin20°
=2(1/2sin80°-√3/2cos80°-sin20°)
=2(sin80°cos60°-cos80°sin60°-sin20°)
=2[sin(80°-60°)-sin20°]
=2(sin20°-sin20°)
=0
Find the value of 3-angle function, cos60 degree, all one point
1/2
Find y = 1 / SiNx + 1 / cosx, X belongs to the minimum value of (0, π / 2)
The book says that y = 1 / SiNx + 1 / cosx > = 2 / (sinxcosx under radical) = 2 radical 2 / radical sin2x > = 2 radical 2. When x = π / 4, Ymin = 2 radical 2. Who will explain
Sinxcosx = sin2x / 2 = 2 / radical (sinxcosx) > = 2 radical 2
Take the equal sign when x = π / 4
y^2=(1/sinx+1/cosx)^2
=(1/(sinxcosx))^2+2(1/(sinxcosx))
=[(1/(sinxcosx))+1]^2-1
=[(2/sin2x)+1]^2-1
>=(2+1)^2-1
=8
Y ^ 2 min = 8
Y min = 2 (root 2)
I think it's a good idea
First divide, then square.. In the square root is required, but pay attention to the value range of X.
What is the sum of sin1 and sin100
First, we introduce a formula: SiNx + siny = sin (x + y) / 2 * cos (X-Y) / 2
Let's go
Sin1 + sin2 +... + sin100 = sin1 + sin51 + sin2 + sin52 +... + sin50 + sin100 can be obtained by adding in pairs here
=2sin26 * cos25 + 2sin27 * cos25 +... + 2sin75 * cos25 bring 2cos25 out
=2cos25 * (sin26 + sin27 +... + sin75) change the order as above
=2cos25 * (sin26 + sin51 + sin27 + sin52 +... + sin50 + sin75) can be obtained by pairing and adding
=2cos25 * (2sin38.5 * cos12.5 + 2sin39.5 * cos12.5 +... 2sin62.5 * cos12.5) brings 2cos12.5 out
=4cos25 * cos12.5 * (sin38.5 + sin39.5 +... + sin62.5) and so on. Since 100 is not the integral power of 2, the result is not easy to simplify. If sin1 is added to sin128, it is easy to simplify
sin1+sin2+...+sin2^n=2^n*cos2^(n-2)*cos2^(n-3)*...*cos2^(-1)*sin[(2^n+1)/2]
such as
sin1+sin2+...+sin128=128cos32*cos16*cos8*cos4*cos2*cos1*cos0.5*sin64.5
Using the integral sum difference formula, 2sin1 / 2 (sin1 +... + sin100) = cos1 / 2-cos3 / 2 + cos3 / 2-cos5 / 2 +... + cos199 / 2-cos201 / 2 = cos1 / 2-cos (201 / 2)
Sin30.45.60 degrees =? Cos30 45 60 degrees =? Cot30 45 60 degrees =?
SIN60=COS30=（√3）/2
SIN45=COS45=（√2）/2
SIN30=COS60=1/2
TAN30=COT60=（√3）/3
TAN45=COT45= 1
TAN60=COT30= √3
30 45 60 angle
sin 1/2 √2/2 √2/3
cos √2/3 √2/2 1/2
tan √3/3 1 √3
cot √3 1 √3/3
If f (cosx) = cosnx, n is even, then f (SiNx)=
Be more detailed···
f(cosx)=cosnx
sinx=cos(x-π/2）
f(sinx)=f[cos(x-π/2)]
=cos(nx-nπ/2)
When n = 4k-2
f(sinx)=-cosnπ
When n = 4K
f(sinx)=cosnπ
K is an integer
If tan80 ° is known to be K, then sin100 ° is equal to?
00tan80°=-tan(180°-80°)=-tan100°=ktan100°=sin100°/cos100°=-kcos100°=sin100°/(-k)sin²100°+cos°100=1sin²100°+[sin100°/(-k)]²=1[(k²+ 1)/k²]sin²100°=1sin²1...
What is the value of Tan 60?
Root 3
Root 3
Root 3
one point seven three two
Radical three
731
Given f (cosx) = SiNx, find f (SiNx)=
F (cosx) = SiNx, so f (COS (π / 2-x)) = f (SiNx) = sin (π / 2-x) = cosx
So f (SiNx) = cosx
There should be two answers to cosx or - cosx
When f is an odd function, f (COS (π / 2-x)) = f (SiNx) = sin (π / 2-x) = cos (x)
When f is an even function, f (SiNx) = f (- SiNx) = f (COS (3 / 2 π - x)) = - cos (x)