How to learn trigonometry well in high school? What is trigonometry used for high school math

Tell you how I did it back then.

Be sure to memorize those formulas, don't look at that simple. Sometimes teachers can make mistakes, and our teachers ask me to memorize them twice a day and write them silently for a certain amount of time. This one is definitely useful, you have all the formulas.

Also, don't do simple questions with 3 corners. That doesn't serve the purpose of training. Do a few more sets of intermediate and high-level questions and understand them thoroughly.

3 corners are absolutely fine. My final score was 144 out of 150 in 3 corners that year, if you have anything else you don't understand, ask me again, trouble the landlord.

To learn trigonometric functions well, remember to memorize the formulas, and be able to reasonably choose the calculation formula to solve the problem, and then be clear about the basic properties of triangles.

I feel that it is also important to have reasonable calculation ability when doing problems, and not to get bored with ......

After all, I am in college, and I was very interested in mathematics at the beginning, but I can't ...... it anymore because of my major

First of all, you have to memorize the formula, and there are some more important deformation formulas, so it shouldn't be difficult to learn them well by doing more questions

Formulas must be memorized, and some routine and tired transformations must be memorized, and more practice should be able to use them flexibly.

Ultimately, it's about practicing more.

Write down more formulas, such as periodicity, monotonicity, heteronymous function transformation, etc., and importantly, draw more trigonometric images.

Trigonometric functions are easy to learn....Formula: Remember, do more questions, the difficulty is according to your own situation, it is recommended to do some puzzles....Thoroughly understood.

Some successful people often laugh at themselves for their poor math scores when they were students, saying that they never figured it out, and they never used anything like sin or cos. It should be said that this is not unrelated to our education. Sometimes our education is too utilitarian, and sometimes it is too detached from reality.

In fact, in daily life, especially if you want to make some measurements, trigonometric functions are very useful and easy to understand.

1 Find the height of the tree by reference.

2 The best way to go to any point on the riverbank to get water, and then to the cowshed.

3 Find the length of the vine that goes around the tree.

4 Measure the height of the mountain.

5. Find the triangle with the shortest circumference of the same base and height between the two lines.

6 Geometric and arithmetic means.

7 Incidence and refraction of light.

8 Measure the width of the lake.

9 Measure the width of the river.

10 average speed.

11 The horizon measures the diameter of the earth.

12 Measure the diameter of the Earth on the summer solstice.

13 Sun altitude, azimuth, hour.

14 Polygons, circles, and maximum area.

Here are some suggestions that may be useful:

Familiarize yourself with basic concepts: Before you start diving into trigonometric functions, make sure you have a good understanding of basic concepts such as sine, cosine, tangent, cotangent, period, etc. If you are not familiar with these concepts enough, it may make subsequent learning more difficult.

Practice drawing diagrams: Try to graph various trigonometric functions, especially periodic and phase difference functions. This can help you better understand the period and amplitude of your function and help you solve problems.

Study the formulas carefully: There are many important formulas for trigonometric functions, such as the doubling formula, the half-angle formula, and the sum difference formula. Carefully studying these formulas and understanding their meaning and usage can help you be more efficient and accurate in solving problems.

Use calculators appropriately: Although calculators may not be available on the exam, the proper use of calculators can help you better understand the concepts and applications of trigonometric functions during your studies. For example, you can use a calculator to verify a formula or draw an image of a function.

Do more practice: Practice is the key to learning trigonometry. Try to do different types of exercises, including solving trigonometric functions, solving trigonometric equations, proving identities, etc. This can help you better grasp the application and theory of trigonometric functions.

Learning trigonometry takes time and effort. In the process of learning, stay patient and motivated, have the courage to try and explore, and I believe that you will gradually grasp the essence of it.

Solution: Because a = b + c -2bccos 60 ° b + c -bc

1) When bc=4, a 2bc-bc = bc = 4a 2, so the minimum value of a is 2;

2) When b+c=4, because: b+c2 (bc) if and only if b=c, the equal sign holds).

So: bc (b+c) 4=4

So a = b + c -bc

b+c)²-3bc

16-3bc≥16-12=4

That is, when b+c=4, a 4, so the minimum value of a is still 2;

3) When b + c = 4, because b + c 2bc then bc 2, -bc -2

So a = b + c -bc4-bc

i.e. a 2 so a 2

Because: a 2 = b 2 + c 2-2bccosa; A is shortest only when b=c.

So: when bc = 4, b=c = 2;Substituting has (amin) 2=b 2+c 2- 8cos60 = 4 + 4 - 4) =4;amin=2

When b + c = 4, b=c = 2; amin = 2 when b 2 + c =4, b = c = 2; amin= √2

Common formulas for trigonometric functions in high school math.

Mathematics Compulsory 4 Common Formulas and Conclusions of Trigonometric Functions I. Trigonometric Functions and Trigonometric Identity Transformations 1. Image and Properties of Trigonometric Functions Functions Sine Functions Cosine Functions Tangent Functions Image Definition Domain r r range [-1,1].

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In a triangle, we know tan a tan b 1, the two numbers multiply more than 0, we know that both numbers are either 0 at the same time, or colleagues are less than 0, assuming that both are greater than 0 at the same time, tan a 0, tan b 0, tan x are between 0-90 degrees, monotonically increasing, because a and b are triangles that the inner angles are definitely greater than 0, and the tangents are both greater than 0, then a, b must be between 0-90°. So it's an acute angle.

Assuming that both are less than 0 at the same time, we know that tan x is at 90-180 degrees, which is also monotonically increasing, but it is less than 0, so at this time, the two angles of a and b must be between 90-180 degrees, but both are triangle inner angles, and it is impossible to have two 90-180 angles at the same time, so it is shot.

In the end, it can be determined that both must be acute angles to be true.

Because the multiplication of two numbers is greater than zero, these two numbers have the same sign, but they cannot both be negative signs, because if the tangent of an angle is negative, then the angle must be obtuse, but in a triangle, it is impossible to have two obtuse angles, so only two are positive numbers, so both are acute angles.

The tangent function is positive on (0, 2) and negative on (2, ).

In the triangle a+b+c=

tana•tanb＞1

Then it must be tana, and tanb are both positive.

So a, b must be acute angles.

Not necessarily, if a and b are both angles less than 45 degrees, then the tangent is less than 1, then the product is also less than 1, isn't it? I don't know if I understand the logic you said wrongly, so why don't you describe it carefully.

Incorrect. If the angle a is less than 45 degrees and the angle b is less than 45 degrees, then tan a<1 and tan b < a*tana<1

This equation does not hold, e.g. in a right triangle, c is a right angle, and tanatanb = 1

There is no such theorem.

The proposition in the topic ** is generally not true, and only in the special case of ab=ac is true, and the special does not serve Liang Stupid Lao Companion can replace the general.

Please see below and click on the slag to enlarge:

Without this theorem, this theorem is often applied to similar triangles, two triangles must have two sets of angles with equal angles in order to be able to judge them as similar triangles, and only one pair of angles in the diagram is equal, so it is impossible to use the knowledge of the proportions of similar triangles to draw this conclusion.