sin 0 = 0 cos 0 = 1 sin 30 = 1/2 cos 30 =√3/2 sin 45 =√2/2 cos 45 =√2/2？
sin 60 =√3/2 cos 60 = 1/2 sin 90 = 1 cos 90 = 0 sin 180 = 0 cos 180 =- 1？
tan 0 = 0 tan 30 =√3/3 tan 45 = 1 tan 60 =√3 tan 180 = 0？
Trigonometric function is a transcendental function in elementary functions in mathematics. Their essence is the mapping between any set of angles and a set of ratio variables. The usual trigonometric function is defined in a plane rectangular coordinate system. Its definition field is the whole real number field. The other is defined in a right triangle, but it is incomplete.
The most basic formula of trigonometric function:
Reciprocal relationship:
tanα cotα= 1
sinα cscα= 1
cosα secα= 1
Relationship between businesses:
sinα/cosα=tanα=secα/cscα
cosα/sinα=cotα=cscα/secα
Square relation:
sin^2(α)+cos^2(α)= 1
1+tan^2(α)=sec^2(α)
1+cot^2(α)=csc^2(α)
Extended data 1. Properties of bounded functions:
Relationship between boundedness of function and properties of other functions
Properties of functions: boundedness, monotonicity, periodicity, continuity and integrability.
① Integrability
Integrable functions on closed intervals must be bounded. Its inverse proposition does not hold water.
② Monotonicity
Monotone functions on closed intervals must be bounded. Its inverse proposition does not hold water.
③ Continuity
A continuous function on a closed interval must be bounded. Its inverse proposition does not hold water.
Second, unbounded function:
An unbounded function is a function that is not bounded. That is to say, the function y=f(x) has only one upper bound (or only one lower bound) on the domain; Or there is neither an upper bound nor a lower bound, and the function in which f(x) is unbounded on the domain is called unbounded function.
The graph of bounded function must be between two straight lines y=-M and y=M parallel to the x axis (when the independent variable is x). Generally speaking, it is not accurate to say that the function is bounded or unbounded, and the interval to be considered must be specified.