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Trigonometric Ratios of Complementary Angles.

First Quadrant

sin(π/2−θ) = cosθ

cos(π/2−θ) = sinθ

tan(π/2−θ) = cotθ

cot(π/2−θ) = tanθ

sec(π/2−θ) = cosecθ

cosec(π/2−θ) = secθ

 

Second Quadrant

sin(π−θ) = sinθ

cos(π−θ) = -cosθ

tan(π−θ) = -tanθ

cot(π−θ) = - cotθ

sec(π−θ) = - secθ

cosec(π−θ) = cosecθ

 

Third Quadrant

sin(π+θ) = -sinθ

cos(π+θ) = -cosθ

tan(π+θ) = tanθ

cot(π+θ) = cotθ

sec(π+θ) = -secθ

cosec(π+θ) = -cosecθ

 

Fourth Quadrant

sin(2π−θ) = -sinθ

cos(2π−θ) = cosθ

tan(2π−θ) = -tanθ

cot(2π−θ) = -cotθ

sec(2π−θ) = secθ

cosec(2π−θ) = -cosecθ

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