The change law of the period of cos is exactly the same as that of sin, except that the period of tanx is π, and the period of atan(ωx+θ) is π/ω, but its absolute value, the part below the X axis and the original part above the X axis are different, so its period is unchanged, that is, the period of | tanx | is π.

According to the relationship between the end edge of the angle in the unit circle and the plane rectangular coordinate system, the end edge of the angle in the unit circle is calculated;

sin(2kπ+α)=sinα=y

The period of ∴sin is 2π.

cos(2kπ+α)=cosα=x

The period of ∴cos is 2π.

Equidistant trigonometric function

(1) square relation:

sin^2(α)+cos^2(α)= 1

tan^2(α)+ 1=sec^2(α)

cot^2(α)+ 1=csc^2(α)

(2) the relationship between products:

sinα=tanα*cosα cosα=cotα*sinα

tanα=sinα*secα cotα=cosα*cscα

secα= tanα* CSCαcsα= secα* cotα