The problem of induction formula Sin (3 / 2 π - θ) how does this translate? There are also similar how to transform? Can you be more specific? How do you think it's in the third quadrant? If 3 / 2 π - θ is 270 ° - θ, it's not sure how much it is. π / 2 + α is in the fourth quadrant. I don't know why

The problem of induction formula Sin (3 / 2 π - θ) how does this translate? There are also similar how to transform? Can you be more specific? How do you think it's in the third quadrant? If 3 / 2 π - θ is 270 ° - θ, it's not sure how much it is. π / 2 + α is in the fourth quadrant. I don't know why

Odd variable even constant, symbol look at quadrant
That is, odd variable and even constant: see how many times of π / 2 it is. If it is odd multiple, it becomes corresponding. That is, sine variable cosine, tangent variable Cotangent, etc. if it is even multiple, it remains unchanged
Sign quadrant, observe the trigonometric function within the whole in the quadrant, can judge positive and negative
Sin (3 / 2 π - θ), 3 / 2 π is an odd multiple of π / 2, so it becomes cosine, and 3 / 2 π - θ is in the third quadrant, so its sine is negative, so the result is - cos θ

The problem of induction formula
Using induced formula to calculate function value
sin（-1574°）
sin（-1574°）
=sin(1800-1574)
=sin226
=sin(180+46)
=-sin46
Why is it negative in the end?

In rectangular coordinates, the unit circle can be drawn,
The sin value is the ordinate of the intersection of the ray and the circle with the specified inclination angle and starting from the origin
226 ° is the third quadrant angle
The ordinate of any point is negative
Therefore, there is a complete two sine three tangent four cosine
It's all pushed out like this

The application of mathematical induction formula
tan10tan20+tan20tan60+tan60tan10=
Write down the process of calculation~

Tan10tan20 + tan20tan60 + tan60tan10 = tan10tan20 + √ 3 (tan20 + tan10) because Tan (30) = Tan (20 + 10) = (tan20 + tan10) / [1-tan20tan10] = √ 3 / 3tan20 + tan10 = √ 3 / 3 * [1-tan20tan10], so: tan10tan20 + tan20tan60 + tan60tan10 = tan10tan20 + √ 3

Come and help! How to calculate the sum of sequence?
For example: when n ≥ 2, TN = 1 + 4 × 3 & ordm; + 6 × 3 ˇ 1 power +. + 2n × 3 ˇ (n-2) power ①
3tn = 3 + 4 × 3 ˇ 1 power + 6 × 3 ˇ 2 power +. + 2n × 3 ˇ (n-1) power
① - 2 get - 2tn = - 2 + 4 + 2 × (3 ˇ 1 power + 3 ˇ 2 power +. 3 ˇ (n-2) power)
How is this converted? Why can't I understand it? I also did some exercises

This is dislocation subtraction, which is suitable for the summation of CN = an * BN (where an is the arithmetic sequence and BN is the proportional sequence) TN = 1 + 4 × 3 & ordm; + 6 × 3 ˇ 1 power +. + 2n × 3 ˇ (n-2) power ① 3tn = 3 + 4 × 3 ˇ 1 power + 6 × 3 ˇ 2 power +. + 2n × 3 ˇ (n-1) power ② (note that the degree of 3 is equal)

1. Granddad Zhang's corn output this year is 20% higher than that of last year. Here, 20% means () is 20% of () output. This should be filled in brackets. 2. A stationery box is 10% lower than the original price. Here, 10% means () is 10% of () price

1. Granddad Zhang's corn output this year is 20% higher than that of last year. The 20% here means that (the increased output) is 20% of (last year's total) output
2. A stationery case is 10% lower than the original price. 10% here means that the price is 10% of the original price

The mathematicians have come to have a look!
1. A, B and C donated books for students in poor areas. The ratio of a to B is 5:6, B to C is 2:3. C donated 40 more books than A. ask 3 how many books to donate for each student
2. To prepare 700 grams of salt water with 6% salt content and 200 grams of salt water with 5% salt content, how many grams of salt water and water with 8% salt content are needed?
3. The distance between a and B is 49 km. A person starts from a place on foot and completes the whole journey in three sections at different speeds. It takes 10 hours. It is known that the speeds of the first section, the second section and the third section are 6 km / h, 4 km / h and 5 km / h respectively, and the distance of the third section is 15 km. How many km is the distance of the first section?
To solve the equation, there must be a calculation process,

1. Set a to donate x copies, B to donate y copies, C to donate Z copies
X:Y=5:6 Y:Z=2:3 Z-X=40
5Y = 6x ①
Y=2Z/3……………… ②
Z-X=40……………………………… ③
Substituting 2 into 1, 5 (2Z / 3) = 6x
∴10Z-18X=0………………… ④
④ - 3 × 10, and 8x = 400
X=50
∴Z=90,Y=60
A: Party A donated 50 copies, Party B donated 60 copies, and Party C donated 90 copies
2. The salt water containing 8% salt should be XG, and the water YG
Already contained salt 200 × 5% = 10g
The required salt is 700 × 6% = 42g
8%X=42-10
X=400g ∴Y=700-400-200=100g
A: slightly
3. ∵ the speed of the third section is 5km / h, the distance is 15km, ∵ the time is 3h, the sum of the distance of the first section and the second section is 49-15 = 34km
Let the time of the first period be XH and the time of the second period be YH
X+Y=7
6X+4Y=34
∴X=3,Y=4
So the first section is 3 × 6 = 18km
A: slightly

Come on!
An ordinary triangle, know the length of three sides are 52m, 36.5m, 27m, can you calculate its height and area? There are detailed steps to answer, bonus points ~!

Helen formula
Suppose there is a triangle with side lengths a, B and C respectively. The area s of the triangle can be obtained by the following formula:
S=√[p(p-a)(p-b)(p-c)]
In the formula, P is the semi perimeter: P = (a + B + C) / 2

At present, there are 10 places recommended to go to university, which are allocated to 7 schools. No school has at least one place. Q: how many ways are there in the allocation of places?

Law one
First, each school is divided into one
The remaining three are divided into seven
one
3=3
There are seven
two
3=2+1
There are 7 * 6 = 42 species
three
3=1+1+1
There are 7 choices, 3 = (7 * 6 * 5) / (3 * 2 * 1) = 35 kinds
There are 7 + 42 + 35 = 84 species
[I haven't done it for a long time, I don't know if I missed it or calculated more]
Method 2
Baffle method
Imagine dividing 10 balls into 7 points with 6 boards
Nine gaps
6 out of 9 = 84

One pocket contains seven white balls and one black ball of different sizes
(1) How many ways can I get three balls out of my pocket?
(2) How many ways can I take three balls out of my pocket, one of which contains a black ball?
(3) How many ways can I take three balls out of my pocket so that they don't contain black balls?
You don't have to fight it out
As long as the train of thought and formula

1. C83 has no conditions, take 3 kinds of 8
2. C72 + C11 7 white take 2 white c72 black C11
3. C73 + C10 7 white take 3 white c73 black C10

[permutation and combination + set of senior high school mathematics]
If a = (0,1,2., m), how many different points are there in the set ((x, y) | x, y belongs to a) in the plane rectangular coordinate system?
The answer is the square of M

X has m choices and y has m choices. Multiplication equals m squared