The document Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev is a part of the SSC Course Quantitative Aptitude for GMAT.

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**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.

**Important Formulae **

**Range of Values of Ratios**

If 0 ≤ θ ≤ 360^{o}, 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.

**Important Results**

**Example.1 Simplify**.

**Sol.**

**Example.2 If cot A **** , find the value of 3 cos A + 4 sin A, where A is in the first quadrant. **

**Sol.**

**Example.3 Find the value of **

**Sol. **

= 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

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