4 trigonometric functions are compulsory in high school, and 4 trigonometric functions are compulsor

y=2sinx x∈r

The maximum value is 2, and the x set {x|x=2k + 2, the minimum value of k z} is -2, and the set of x {x| x=2kπ-π/2,k∈z}y=2-cosx/3， x∈r

When x 3 = 2k ,k z, i.e. x = 6k ,k z, cosx 3 obtains the maximum value of 1 and y obtains the minimum value of 1

y gets the minimum value of 1, and the set of x {x|x=6k,k z} when x 3=2k + k z, i.e., x=6k +2, k z, cosx 3 obtains the minimum value -1, and y obtains the maximum value of 3

y gets the minimum value of 3, and the set of x {x|x=6k +2 ,k z} is given by 2k + 2 2x+2 2k +3 2 2 2x 2k +5 4, k zk + 8 2x k +5 8, k z function monotonically decreasing interval.

kπ+π/8,kπ+5π/8]，k∈z

Trigonometric functions are a common class of functions about angles in mathematics. It can also be said that the function with the angle as the independent variable and the ratio of the angle corresponding to any two sides as the dependent variable is called the trigonometric function, which relates the inner angle of the right triangle with the ratio of the length of its two sides, and can also be defined equivalently by the length of various line segments related to the unit circle. Trigonometric functions play an important role in the study of the properties of geometric shapes such as triangles and circles, and are also a fundamental mathematical tool for the study of periodic phenomena.

In mathematical analysis, trigonometric functions are also defined as infinite limits or solutions to specific differential equations, allowing their values to be extended to arbitrary real values, even complex values.

Common trigonometric functions include sine, cosine, and tangent. In other disciplines such as navigation, surveying and mapping, and engineering, other trigonometric functions such as cotangent function, secant function, cosecant function, sagittal function, cosagittal function, semi-sagittal function, semi-cosagittal function, and other trigonometric functions are also used. The relationship between different trigonometric functions can be determined by geometrical intuition, or by calculation, and is called trigonometric identities.

Trigonometric functions are generally used to calculate the edges of unknown lengths and unknown angles in triangles, and have a wide range of uses in navigation, engineering, and physics. In addition, using trigonometric functions as a template, a similar class of functions can be defined, called hyperbolic functions. The common hyperbolic function is also known as hyperbolic sine function, hyperbolic cosine function, and many more.

Trigonometric functions (also known as circular functions) are functions of angles; They are important in studying triangles and modeling periodic phenomena and many other applications. Trigonometric function is usually defined as the ratio of the two sides of a right triangle containing this angle, and can also be defined equivalently as the length of various line segments on a unit circle. More modern definitions express them as infinite series or solutions to specific differential equations, allowing them to extend to arbitrary positive and negative values, even complex values.

1> ymax=2, at this point x set {x| x=2kπ+π/2,k∈z}

ymin=-2, at which point x set {x| x=2kπ-π/2,k∈z}

Special angular trigonometric values.

sin0=0

sin30=

sin45 = 2 of the root of the half

sin60 = Root of the second half number 3

sin90=1

cos0=1

cos30 = Root number 3 of the halfs

cos45= 2 of the root of the half

cos60=

cos90=0

tan0=0

tan30 = 3 thirds of the root number

tan45=1

tan60= root number 3

tan90=None.

cot0 = none.

cot30 = root number 3

cot45=1

cot60 = 3 of the root of thirds

cot90=0

2) Trigonometric values of any angle of 0° 90°, check the trigonometric function table. (3) Changes in the value of acute trigonometric functions.

i) Acute trigonometric values are all positive.

ii) When the angle varies between 0° and 90°, the sinusoidal value increases (or decreases) as the angle increases (or decreases).

The cosine decreases (or increases) with an increase (or decreases) with an angleThe tangent increases (or decreases) with an angleThe cotangent decreases (or increases) with an increase (or decrease) with an angle (iii) when the angle varies between 0° 90°, 0 sin 1, 1 cos 0, and when the angle varies between 0° < 90°, tan >0, cot >0

"Acute trigonometry" belongs to trigonometry, which is an important part of the field of "space and graphics" in the Mathematics Curriculum Standards. According to the "Mathematics Curriculum Standards", the content of trigonometry in secondary school mathematics is divided into two parts, the first part is placed in the third stage of compulsory education, and the second part is placed in the high school stage. In the third stage of compulsory education, the content of acute trigonometric functions and solving right triangles is mainly studied, and the content of this set of textbooks is arranged in one chapter, which is the chapter "Acute Trigonometric Functions".

Trigonometry in high school is the main part of trigonometry, including solving oblique triangles, trigonometric functions, inverse trigonometric functions, and simple trigonometric equations. Whether it is from the point of view of content, or from the point of view of the way of thinking about the problem, the former part is an important foundation for the latter part, and mastering the concept of acute trigonometric functions and the method of solving right triangles is an important preparation for learning trigonometric functions and solving oblique triangles.

You can put cos 2 first

90 degrees and cos2

180 degrees. Calculate out = 1

The first cos 21 degrees and .

The last item cos 2

179 sum = 2cos2

1 degree, and so on, the original becomes: 2 (cos 2

1 degree + cos 2

2 degrees +.cos^2

89 degrees) +1

Then take out the first and last terms: cos 2

1 degree + cos 2

89 degrees = 1 and so on, the original becomes: 2 (44 + cos 2

45 degrees) +1 = 90

See if the answer is right?

Hope it helps

In any case, the trigonometric function y=sin( x+ ) is in the range of [-1,1], if y=asin( x+ ) then the range is [-a,a] max is the opposite of min, and ymax-ymin=2a a=4 y=asin( x+ ) is [-4,4]. Again, y=asin(x+)b's range is [1,9], so b=5. ∵t/2=(14-2=)12，∴ω=π/12.

Let y=0 then = 3 y=4sin( 12*x- 3 )+5 m market.