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

Quantitative Aptitude for GMAT

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

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

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

 

SOME MORE RESULTS:

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

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

 

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


Sol.

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


Ex.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


Ex.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


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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