Definitions and Formulas
- An angle is positive if it is measured in the anticlockwise direction and negative if it is measured in the clockwise direction.
- In a right triangle ABC, right-angled at B
- If one of the trigonometric ratios of an acute angle is known, the remaining trigonometric ratios can be determined.
- Two angles are said to be complementary if their sum is 90°, and each one of them is called the complement of the other.
sin (90° - θ) = cos θ
cos (90° - θ) = sin θ
tan (90° - θ) = cot θ
cot (90° - θ) = tan θ
sec (90° - θ) = cosec θ
cosec (90° - θ) = sec θ
An equation with trigonometric ratios of an angle θ, which is true for all values of ‘θ’, for which the given trigonometric ratios are defined, is called an identity.
Three fundamental trigonometric identities are
(a) sin2θ + cos2θ = 1
(b) sec2θ = 1 + tan2θ
(c) cosec2θ = 1 + cot2θ
Table: Values of trigonometric ratios of 0°, 30°, 45°, 60° and 90°