Special values commonly used in high school mathematics

These are some special functions. Take a look and remember it when it's cooked.

(1) trigonometric function value of special angle

sin0=0

sin30=0.5

Sin45=0.707 1 radical number 2

Sin60=0.8660, and the root of two is 3.

sin90= 1

cos0= 1

Cos30=0.866025404 Two-thirds root number 3

Cos 45 = 0.707106781,two and a half root signs.

cos60=0.5

cos90=0

tan0=0

Tan30=0.577350269 root number 3

tan45= 1

Tan 60 = 1.7050808 root number 3

Tan90= None

Cot0= none

Cot30 = 1.750808 root number 3

cot45= 1

Cot60=0.577350269 root number 3

cot90=0

(2) Check the trigonometric function value at any angle from 0 to 90. (See below)

(3) the change of the value of acute trigonometric function

(i) The values of acute trigonometric functions are all positive.

(ii) When the angle changes from 0 to 90 degrees,

Sine value increases (or decreases) with the increase (or decrease) of angle.

The cosine value decreases (or increases) with the increase (or decrease) of the angle.

The tangent value increases (or decreases) with the increase (or decrease) of angle.

The cotangent value decreases (or increases) with the increase (or decrease) of angle.

(iii) When the angle varies between 0 and 90,

0≤sinα≤ 1， 1≥cosα≥0，

When the angle is 0.

tanα& gt； 0，cotα& gt； 0.

"Acute trigonometric function" belongs to trigonometry and is an important content in the field of "space and graphics" of mathematics curriculum standard. According to the mathematics curriculum standard, middle school mathematics divides trigonometry into two parts, the first part is in the third stage of compulsory education, and the second part is in the high school stage. The third stage of compulsory education mainly studies the content of acute triangle function and the solution of right triangle. This textbook has a chapter called "Acute Trigonometric Function". Trigonometry in senior high school is the main part of trigonometry, including solving oblique triangles, trigonometric functions, inverse trigonometric functions and simple trigonometric equations. The former part is the important foundation of the latter part, both in content and way of thinking. Mastering the concept of acute trigonometric function and the method of solving right triangle is an important preparation for learning trigonometric function and solving oblique triangle.

Attachment: trigonometric function value table

sin0=0，

sin 15=(√6-√2)/4，

sin30= 1/2，

sin45=√2/2，

sin60=√3/2，

sin75=(√6+√2)/2，

sin90= 1，

sin 105 =√2/2 *(√3/2+ 1/2)

sin 120=√3/2

sin 135=√2/2

sin 150= 1/2