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 .