Trigonometric Function for θ > 360 degree
If we rotate ( clockwise or anticlockwise ) line OP by 360 o , it will come back to same position . Thus if θ increases ( or decreases ) by any integral multiple of 2π , the values of sine and cosine functions do not change . Thus ,
sin ( 2nπ + θ ) = sinθ , n ∈ Z ,
cos ( 2nπ + θ ) = cosθ , n ∈ Z tan ( 2nπ + θ ) = tanθ , n ∈ Z
Note that , in the above scenario , Sinθ = b / 1 = b , cosθ = a / 1 = a & tanθ = b / a .
Also , in right Triangle POM , a 2 + b 2 = 1 Using these 2 equations we can say that sin 2 θ + cos 2 θ = 1 Also we can prove that o o
1 + tan 2 θ = sec 2 θ 1 + cot 2 θ = cosec 2 θ