Given that 0 ＜ a ＜ Wu / 2, cos (a + Wu / 6) = 3 / 5, find cosa?

Given that 0 ＜ a ＜ Wu / 2, cos (a + Wu / 6) = 3 / 5, find cosa?

Because 0
cosa=3/5,0
cosa=3/5
Zero
If cos (a + π / 6) = 2 / 3 and a is an acute angle, cosa can be obtained
Cos (a + π / 6) = 2 / 3 A + π / 6 ranges from π / 6 to 2 π / 3 sin (a + π / 6) = 5 / 3
√3/2cosa-1/2sina=2/3 （1）
√3/2sina+1/2cosa=√5/3（2）
(1) X √ 3 + (2) is 2cosa = 2 √ 3 + √ 5 / 3
cosa=（2√3+√5）/6
cos(a+π/6)=√3/2cosa-1/2sina=2/3
√3/2cosa-2/3=1/2sina
3/4cos^2a-6cosa+4/9=1/4-1/4cos^2a
cos^2a-6cosa+25/36=0
(cosa-3)^2-299/36=0
Then cosa = 3 - √ 299 / 6
Or cosa = 3 + √ 299 / 6
Cosa * cos30 ° - Sina * sin30 ° = 2 / 3, so - Sina * sin30 ° = 2 / 3-cosa * cos30 °, so both sides of the equation are squared at the same time, and the square of SiNx is expressed as 1-cosx ^ 2, then the univariate quadratic equation about cosx can be obtained, and the solution can be obtained
cosa
Cos (a + b) = - 1 / 3, sin (a + b) = 2 radical 2 / 3
cos2a=-5/13，sin2a=12/13
cos(a-b)=cos[2a-(a+b)]
=cos2acos(a+b)+sin2asin(a+b)
=5 / 39 + 24 root 2 / 39
=(5 + 24 radical 2) / 39
It is known that a focal coordinate of the hyperbola is (0. - 13), and the absolute value of the difference between the distances between a point P and two focal points on the hyperbola is 24. The standard square of the hyperbola is obtained
Is the centrosymmetric point the origin?
Let the hyperbolic equation be y ^ 2 / b ^ 2-x ^ 2 / A ^ 2 = 1,
Let the two focus points be F1 and F2,
||PF1|-|PF2||=24,
According to the hyperbola theorem, 2b = 24, B = 12,
c=13,
a^2=c^2-b^2=25,
The hyperbolic equation is y ^ 2 / 144-x ^ 2 / 25 = 1
The range of SiNx in y = SiNx absolute value
sinx>=0
y=sinx-sinx=0
sinx
The distance between a point m on hyperbola x ^ 2 / 9-y ^ 2 / 7 = 1 and focus F1 is 2
If n is the midpoint of MF1 and O is the origin, how long is on
Four
Draw, MF2, no is the median line of triangle f1mf2
Mf2-mf1 = 2A = 6 (hyperbolic definition)
Then the value of sincoxy + sincoxy is 0?
sinx+siny=-sinz (1)
cosx+cosy=-cosz (2)
(1)^2+(2)^2
=>2+2sinxcosx+2cosxcosy=1
=>cos(x-y)=cosxcosy+sinxsiny=-1/2
sinx+siny=-sinz
cosx+cosy=-cosz
The square of the first formula plus the square of the second formula
(sinx)^2+2sinxsiny+(siny)^2+(cosx)^2+2cosxcosy+(cosy^2=1
2+2cos（x-y)=1
cos（x-y）=-1/4
Given the focal point F1 (5,0) F2 (negative 5,0), the absolute value of the distance difference between a point P on the hyperbola and F1, F2 is equal to 6
Given the focus F1 (5,0) F2 (negative 5,0), the absolute value of the distance difference between a point P on the hyperbola and F1, F2 is equal to 6. The standard equation for finding the hyperbola is to find the hyperbola equation which is in common focus with the ellipse x ^ 2 / 25 + y ^ 2 / 5 = 1 and passes through the point (3 root sign 2, root sign 2)
1、
2a=6
A=3
b²=16
x²/9-y²/16=1
2、
Ellipse a '& sup2; = 25, B' & sup2; = 5
c'²=20
In hyperbola C & sup2; = 20
x²/a²-y²/(20-a²)=1
18/a²-2/(20-a²)=1
a^4-40a²+360=0
a²=20-2√10
x²/(20-2√10)-y²/(2√10)=1
it's too hard
1. C = 5,2a = 6, a = 3, B = 4, standard equation x ^ 2 / 9-y ^ 2 / 16 = 1
2. C = 2 radical 5, over point (3 radical 2, radical 2), maybe the title is wrong
Given SiNx + siny = 1, what is the range of cosx + cosy?
Given SiNx + siny = 1, find the value range of cosx + cosy
Let t = cosx + cosy 2
sinx+siny=1 ①
Add the square of two formulas again
t^+1=2+2sinxsiny+2cosxcosy
t^=2cos(x-y)+1
-1≤t^≤3
0 ≤ T ^ ≤ 3
- radical 3 ≤ cosx + cosyt ≤ radical 3
Square addition
It is concluded that (SiNx + siny) ^ 2 + (cosx + cosy) ^ 2 = 1 + 1 + 2 (sinxsiny + cosxcosy) = 2 + 2cos (X-Y)
So (cosx + cosy) ^ 2 = 1 + 2cos (X-Y) is greater than or equal to 0 and less than or equal to 3
So cosx + cosy is greater than or equal to negative root 3 and less than or equal to root 3
2. According to the following hyperbolic equation, judge the focus position, and calculate the absolute value of the difference between any point on the hyperbola and two focus distances and the focus coordinates
(1)(x^2/18)-(y^2/9)=1;
(2)15y^2-x^2=15;
(3)(x^2/6)-(y^2/3)=2.
3. In hyperbola, calculate:
(1) Given a = 7, B = 5, find C;
(2) Given a + B = 9, A-B = 3, find C
4. Find the standard equation of hyperbola suitable for the following conditions:
(1) A = 3, B = 4, the focus is on the y-axis;
(2) B = 3, a focal coordinate is (- 5,0);
(3) The focus is on the x-axis, C = root 15, and passes through the point P (3, 2, 6);
(4) The focal length is 10, and the absolute value of the distance difference between one point and two focal points on the hyperbola is 8;
(5) A = 3, passing through point P (6, root 3)
2 (1) (plus or minus 3 root sign 3,0) 2A = 6 root sign 2 (2) (0, plus or minus 4) 2A = 2 (3) (plus or minus 3 root sign 2,0) 2A = 4 root sign 33 (1) C = 2 root sign 15 (2) C = 3 root sign 54 (1) y ^ 2 / 9 - (x ^ 2 / 16) = 1 (2) (x ^ 2 / 16) - (y ^ 2 / 9) = 1 (3) (x ^ 2 / 9) - (y ^ 2 / 6) = 1 (4) (x ^ 2 / 16