Its image only needs to turn the part below the X axis in the sine function image to the above X axis symmetrically, and its parity, periodicity and monotonicity can be intuitively seen from the image.

Parity x:R is symmetrical about the origin.

f(-x)=/sin(-x)/=/-sinx/=/sinx/= f(x)

Is an even number function.

Periodicity: T=2pai/2=pai

3. Monotonicity from the Image Mountain

Monotonic increase in [kpai, pai/2+kpai]

On [kpai+pai/2, kpai+pai]: K:Z monotonically decreasing.

trigonometric function

Trigonometric function is a kind of transcendental function in elementary function in mathematics. Their essence is the mapping between the set of arbitrary angles and a set of ratio variables. The usual trigonometric function is defined in the plane rectangular coordinate system, and its domain is the whole real number domain. The other is defined in a right triangle, but it is incomplete. Modern mathematics describes them as the limit of infinite sequence and the solution of differential equation, and extends their definitions to complex system.