Trigonometry
Trigonometric Ratios
For the right ΔABC, right-angled at ∠B, the trigonometric ratios of the ∠A are as follows:
sin A=opposite side/hypotenuse=BC/AC
cos A=adjacent side/hypotenuse=AB/AC
tan A=opposite side/adjacent side=BC/AB
cosec A=hypotenuse/opposite side=AC/BC
sec A=hypotenuse/adjacent side=AC/AB
cot A=adjacent side/opposite side=AB/BC
Relation between Trigonometric Ratios
cosec θ =1/sin θ
sec θ = 1/cos θ
tan θ = sin θ/cos θ
cot θ = cos θ/sin θ=1/tan θ
Complementary Trigonometric ratios
If θ is an acute angle, its complementary angle is 90∘−θ.
The following relations hold true for trigonometric ratios of complementary angles.
sin (90∘− θ) = cos θ
cos (90∘− θ) = sin θ
tan (90∘− θ) = cot θ
cot (90∘− θ) = tan θ
cosec (90∘− θ) = sec θ
sec (90∘− θ) = cosec θ
Trigonometric Identities
sin2θ+cos2θ=1
1+cot2θ=coesc2θ
1+tan2θ=sec2θ