Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev

Quantitative Aptitude for GMAT

SSC : Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev

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Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev

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.
    Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev

Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev


Basic Trigonometric Ratios

  • In a right triangle ABC, if θ be the angle between AC & BC.
    Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev
  • 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.
    Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev

Important Formulae 

Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev

Range of Values of Ratios

If 0 ≤ θ ≤ 360o, then the values for different trigonometric ratios will be as follows: 

  1. - 1 ≤ Sin θ ≤ 1
  2. - 1 ≤ cos θ ≤ 1
  3. - ∞ ≤ tan θ ≤ ∞
  4. - ∞ ≤ cot θ ≤ ∞
  5. - ∞ ≤ Sec θ ≤ -1    &       1 ≤ Sec θ ≤ ∞
  6. - ∞ ≤ Cosec θ ≤ - 1     &      1 ≤ Cosec θ ≤ ∞

Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev


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.

Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev

 

Important Results

Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev

Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev

 

Example.1 Simplify.
Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev

Sol.

Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev


Example.2 If cot A Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev , find the value of 3 cos A + 4 sin A, where A is in the first quadrant. 

Sol.

Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRevTrigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRevTrigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev


Example.3 Find the value of 

Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev

Sol. 

Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev
= 1 + 1 - 1 = 1


Table: Values of trigonometric Ratio for some special angles.

Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev


Properties of Triangle

➢ Sine Rule

  • In any triangle ABC if AB, BC, AC be represented by c, a, b respectively
    Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev
    Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev

➢ Cosine Rule

  • In a triangle ABC of having sides of any size, we have the following rule:
    Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev
    Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev
    Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev

 ➢  Area of Triangle

Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev

 

Trigonometry - Examples (with Solutions), Geometry, Quantitative Aptitude CAT Notes | EduRev

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