Trigonometry is that branch of Mathematics which deals with the measurement of the sides and the angles of a triangle and the problems related to angles. Ratios of the sides of a triangle with respect to its acute angles are called trigonometric ratios.
In the right angled ∆AMP, for acute angle PAM = θ
- Base = AM = x
- Perpendicular = PM = y
- Hypotenuse = AP = r
- sin θ = y/r
- cos θ = x/r
- tan θ = y/x
- cosec θ = r/y
- sec θ = r/x
- cot θ = x/y
If two sides of any right triangle are given, then all the six trigonometric ratios can be written. If one trigonometric ratio is given, then other trigonometric ratios can be written by using pythagoras theorem or trigonometric identities.
An equation involving trigonometric ratios of an angle θ is said to be a trigonometric identity if it is satisfied for all values of θ for which the given trigonometric ratios are defined.
- sin2θ + cos2θ = 1
- 1 + tan2θ = sec2θ
- 1 + cot2θ = cosec2θ
Complementary angles: If θ is an acute angle, then
- sin (90º - θ) = cos θ and cos (90º - θ) = sin θ
- tan (90º - θ) = cot θ and cot (90º - θ) = tan θ
- cosec (90º - θ) = sec θ and sec (90º - θ) = cosec θ