Angles and their Relationship
- Angles are measured in many units’ viz. degrees, minutes, seconds, radians, gradients.
- Where 1 degree = 60 minutes, 1 minute = 60 seconds,
π radians = 180° = 200g
⇒ 1 radian = 180°/π and 1 degree = π/ 180 radians.
Basic Trigonometric Ratios
- In a right triangle ABC, if θ be the angle between AC & BC.
- If θ is one of the angle other then right angle, then the side opposite to the angle is perpendicular (P) and the sides containing the angle are taken as Base ( B) and the hypotenuse (H). In this type of triangles, we can have six types of ratios. These ratios are called trigonometric ratios.
Range of Values of Ratios
If 0 ≤ θ ≤ 360o, then the values for different trigonometric ratios will be as follows:
- - 1 ≤ Sin θ ≤ 1
- - 1 ≤ cos θ ≤ 1
- - ∞ ≤ tan θ ≤ ∞
- - ∞ ≤ cot θ ≤ ∞
- - ∞ ≤ Sec θ ≤ -1 & 1 ≤ Sec θ ≤ ∞
- - ∞ ≤ Cosec θ ≤ - 1 & 1 ≤ Cosec θ ≤ ∞
Sign of Trigonometric Ratios
We divide the angle at a point (i.e. 360°) into 4 parts called quadrants. In the first quadrant all the trigonometric ratios are positive.
Example.2 If cot A , find the value of 3 cos A + 4 sin A, where A is in the first quadrant.
Example.3 Find the value of
= 1 + 1 - 1 = 1
Table: Values of trigonometric Ratio for some special angles.
Properties of Triangle
➢ Sine Rule
- In any triangle ABC if AB, BC, AC be represented by c, a, b respectively
➢ Cosine Rule
- In a triangle ABC of having sides of any size, we have the following rule:
➢ Area of Triangle