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