Page 8 - 11-Math-10 Trigonometric Identities

110. .QTuriagdornaotmiceEtrqicuaIdteionntisties eeLLeeaarrnn..PPuunnjjaabb

s=in  π2 -θ  cosθ , =cos π2 -θ  sin θ , =tan  π2 -θ  cotθ

sin  π +θ  =cosθ , cos  π + θ  =- sin θ , tan  π +θ  =- cot θ
 2  2   2 

sin(π -θ ) =sin θ , cos(π -θ ) =-cosθ , tan(π -θ ) =- tanθ
sin(π + θ ) =-sinθ , cos(π + θ ) =-cosθ , tan(π + θ ) =tanθ

sin  3π - θ  =- cosθ , cos  3π -θ  =- sin θ , tan  3π -θ  =cotθ
 2   2   2 

sin  3π   3π   3π 
 2 +θ  =- cosθ , cos  2 +θ  =sinθ , tan  2 + θ  =- cot θ

sin(2π -θ ) =-sinθ , cos(2π -θ ) =cosθ , tan(2π -θ ) =- tanθ
=sin(2π + θ ) sinθ , =cos(2π + θ ) cosθ , =tan(2π + θ ) tanθ

Note: The above results also apply to the reciprocals of sine, cosine and tangent. These
results are to be applied frequently in the study of trigonometry, and they can be
remembered by using the following device:

1) If θ is added to or subtracted from odd multiple of right angle, the trigonometric
ratios change into co-ratios and vice versa.
i.e, sin ←→cos, tan ←→cot, sec←→coses

e.=g. sin  π2 -θ  cosθ an=d cos 32π + θ  sinθ

2) If θ is added to or subtracted from an even multiple of π the trigonometric ratios shall
2
remain the same.

3) So far as the sign of the results is concerned, it is determined by the quadrant in which
the terminal arm of the angle lies.
e.g. s=in(π -θ ) sinθ , t=an(π + θ ) tan θ , co=s(2π -θ ) cos θ

version: 1.1

8