Let’ s take a xy plane & draw a circle with radius( PO) 1 cm & center as center of xy plane. Since one complete revolution subtends an angle of 2π radian at the centre of circle, ∠AOB = π / 2, ∠AOC = π and ∠AOD = 3π / 2. All angles which are integral multiples of π / 2 are called quadrantal angles. Let us name these quadrants as Quadrant I, II, III & IV.
In Triangle POM( Quadrant I), Sinθ = b / 1 = b, cosθ = a / 1 = a & tanθ = b / a.
Now rotate the line PO anticlockwise & observe values of Sinθ, Cosθ & Tan θ.
You will observe that 1. In Quadrant I, all Sinθ, Cosθ & Tan θ are all positive. 2. In Quadrant II only Sinθ is positive 3. In Quadrant III only Tanθ is positive 4. In Quadrant IV only Cosθ is positive
Signs of Cosec θ, Sec θ & Cot θ can easily be determined using signs of Sinθ, Cosθ & Tan θ respectively.