Let a = (3sina, COSA), B = (2sina, 5sina-4cosa), a ∈ (3 π 2, 2 π), and a ⊥ B. find the values of Tana and COS (a + π 3)

Let a = (3sina, COSA), B = (2sina, 5sina-4cosa), a ∈ (3 π 2, 2 π), and a ⊥ B. find the values of Tana and COS (a + π 3)

From the meaning of the title, we can get a. B = 6sin2a + 5sinacosa-4cos2a = 0, ∵ that is, (3sina + 4cosa) (2sina COSA) = 0, that is, 3sina + 4cosa = 0 & nbsp; we can get Tana = - 43; or: 2sina cosa = 0, we can get Tana = 12. ∵ a ∈ (3 π 2, 2 π), ∵ Tana < 0, ∵ only Tana = - 4
Given Tana = 2. Find the value of 2sina cosa of 3sina + 4cosa,
Given Tana = 2. Find the value of 2sina cosa of 3sina + 4cosa
2sina cosa of 3sina + 4cosa
=Cosa (3tana + 4) of cosa (2tana-1)
=(3tana + 4) of (2tana-1)
=(2 * 2-1) (3 * 2 + 4)
=3 out of 10
How to judge the roots of the imaginary number equation
Eg
How many roots does the imaginary equation: Z ^ 2 - 2 * Z + I = 0 have?
The original equation is: (Z-1) ^ 2 = 1-I, let Z-1 = a + bi (AB real number)
The equation is as follows
a^2-b^2-1+(2ab+1)i=0 =>
a^2-b^2-1=0
2ab+1=0
Solution (can't write down, solve it yourself): (a, b) has two values, so there are two solutions
(sin3x+sinx)/(cos3x+cosx)=
sinα+sinβ=2sin[(α+β)/2]cos[(α-β)/2]
cosα+cosβ=2cos[(α+β)/2]cos[(α-β)/2]
So:
(sin3x+sinx)/(cos3x+cosx)
=2sin2xcosx/(2cos2xcosx)
=sin2x/cos2x
=tam2x
(sin3x+sinx)/(cos3x+cosx)
=2sin2xcosx/(2cos2xcosx)
=tan2x
Is 0 real or imaginary or pure imaginary?
real number
SiNx is used to represent sin3x and cosx is used to represent cos3x
Cos3x = 4cosx minus 3cosx
What are real numbers and imaginary numbers
Real numbers include rational numbers and irrational numbers. Irrational numbers are infinite acyclic decimals, while rational numbers include integers and fractions
In mathematics, real number is directly defined as the number one by one corresponding to the point on the number axis. Originally, real number was only called number. Later, the concept of imaginary number was introduced. The original number was called "real number" - meaning "real number"
Real numbers can be divided into rational numbers and irrational numbers, or algebraic numbers and transcendental numbers, or positive numbers, negative numbers and zero. The set of real numbers is usually represented by the letter R or R ^ n. R ^ n represents n-dimensional real number space. Real numbers are uncountable
In mathematics, the number whose square is negative is defined as pure imaginary number. All imaginary numbers are complex numbers. It is defined as I ^ 2 = - 1. But imaginary numbers have no arithmetic root, so √ (- 1) = ± I. for Z = a + bi, it can also be expressed as the form of IA power of E, where e is a constant, I is the imaginary unit, and a is the argument of the imaginary number, It can be expressed as Z = cosa + isina. A logarithm composed of real number and imaginary number is regarded as a number in the range of complex number and named as complex number. Imaginary number has no positive or negative to speak of. The complex number that is not real number can not be compared even if it is pure imaginary number
This kind of number has a special symbol "I" (imaginary), which is called the imaginary unit. However, in the electronic industry, because I is usually used to represent the current, the imaginary unit is represented by J
The standard equation for an ellipse with a focus of parabolic y2 = 8x and a eccentricity of 12 is ()
A. x216+y212＝1B. x212+y216＝1C. x216+y24＝1D. x24+y216＝1
From the meaning of the question, we can get that the focus is (2,0), so C = 2. Then from CA = 12 & nbsp; we can get a = 4, B = 23. So the standard equation of ellipse is x216 + y212 = 1
The relationship between imaginary number and real number
Imaginary number + imaginary number =?
Imaginary number + real number =?
Imaginary number * imaginary number =?
Imaginary / imaginary =?
Imaginary number * real number =?
Imaginary / real =?
The root of an imaginary number?
A number in the form of Z = a + IB (a, B are real numbers) is called a complex number. A is the real part of Z, denoted by rel (z) = a, B is the imaginary part of Z, denoted by img (z) = B. when B is nonzero, Z is called an imaginary number. I is a root of x ^ 2 = - 1, which is called an imaginary unit
The operation of imaginary numbers is identical with that of real numbers, which satisfies the combination law, distribution law and commutation law. We can treat imaginary numbers as polynomials, but I ^ 2 = - 1 can simplify them
The complex field is an extension of the real field
The imaginary number square root adopts the method of real number square root
Imaginary + imaginary = imaginary or real
Imaginary + real = imaginary
Imaginary number * imaginary number = imaginary number or real number
Imaginary / imaginary = imaginary or real
Imaginary * real = imaginary or real
Imaginary / real = imaginary
The root of an imaginary number is an imaginary number
Real numbers contain imaginary numbers. The general formula of imaginary numbers is a + bi. A is the real part, that is, the real part. Bi is the imaginary part. B is the real number. I is the unique symbol of imaginary numbers
Imaginary + imaginary = imaginary or real
Imaginary + real = imaginary
Imaginary number * imaginary number = imaginary number or real number
Imaginary / imaginary = imaginary or real
Imaginary number * real number = imaginary number or real number (0)
Imaginary / real = imaginary
The root of an imaginary number is an imaginary number
They are all plural
The general formula of imaginary number is a + bi, a is the real part, that is, the real part, Bi is the imaginary part, B is the real number, and I is the unique symbol of imaginary number
In addition and subtraction, the real part and the real part are added and subtracted, and the imaginary part and the imaginary part are added and subtracted;
Multiplication and division are calculated by the distribution law similar to real number, I ^ 2 = - 1;
The square root of imaginary number is square root of real number.
Imaginary + imaginary = imaginary or real
Imaginary + real = imaginary
Imaginary number * imaginary number = imaginary number or real number
Imaginary / imaginary = imaginary or real
Imaginary number
The general formula of imaginary number is a + bi, a is the real part, that is, the real part, Bi is the imaginary part, B is the real number, and I is the unique symbol of imaginary number
In addition and subtraction, the real part and the real part are added and subtracted, and the imaginary part and the imaginary part are added and subtracted;
Multiplication and division are calculated by the distribution law similar to real number, I ^ 2 = - 1;
The square root of imaginary number is square root of real number.
Imaginary + imaginary = imaginary or real
Imaginary + real = imaginary
Imaginary number * imaginary number = imaginary number or real number
Imaginary / imaginary = imaginary or real
Imaginary * real = imaginary or real
Imaginary / real = imaginary
The root of an imaginary number is an imaginary number
Imaginary number + real number
Imaginary + real = imaginary
It is known that there are four intersections between parabola y = x * X-2 and ellipse x * x / 4 + y * y = 1. The equation of the circle with these four intersections is solved
What are the four simple ways to find the intersection?
A common way to solve this kind of problem is to find out the four intersection points of parabola and ellipse, and substitute them into the circular equation (x-a) ^ 2 + (y-b) ^ 2 = R ^ 2 to solve the radius of the center of the circle. However, there is a very simple way to solve this problem. The parabolic equation x ^ 2-y = 2 (1) the elliptic equation x ^ 2 / 4 + y ^ 2 = 1 (2) multiply equation (1) by 3 / 4 plus equation (2) to get x ^ 2 + y ^ 2 -