Let a rotating line OA rotates about O in the anti-clockwise direction, from initial position to finishing position provides an angle ∠XOA = θ again the exact same rotating heat rotates in the same direction and makes an angle ∠AOB =90°.

Take a point C top top OA and also draw CD perpendicular come OX or OX’.

Again, take it a allude E top top OB such the OE = OC and draw EF perpendicular to OX or OX’. Indigenous the right-angled ∆ OCD and also ∆ OEF us get,

∠COD = ∠OEF

and OC = OE.

Therefore, ∆ OCD ≅ ∆ OEF (congruent).

Therefore according to the meaning of trigonometric sign, the = - DC, FE = OD and also OE = OC

We observe that in chart 1 and 4 OF and also DC room opposite signs and also FE, OD room either both positive. Again us observe that in diagram 2 and also 3 OF and also DC are opposite signs and FE, OD are both negative.

According to the an interpretation of trigonometric ratio we get,