**SSC CHSL Topic Wise Study Material – Quantitative Aptitude – Basic Trigonometry**

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The word trigonometry is derived from the Greek words ‘tri’ meaning three, ‘gon’ meaning sides and ‘metron’ meaning measure.

Infact, trigonometry is the study of the relations between the sides and angles of triangles.

**Degree and Radian Measures**

Degree and radian are the unit for measuring an angle, where angle subtended at the centre by an arc of length. 1 unit in a circle of radius 1 unit, is said to have a measure of 1 radian.

Radian measure = π/180° x Degree measure

Degree measure = 180°/π x Radian measure

**Example Find the degree measure corresponding to (2π/15) ^{c}**

(a) 24°

(b) 45°

(c) 50°

(d) 25°

**Trigonometric Ratios**

The ratios between different sides of a right angled triangle with respect to its acute angles are Called trigonometric ratios.

Let us consider ∠A of ΔABC to represent trigonometric ratios.

**Relation Between Trigonometric Ratios**

**Trigonometric Ratios of Some Specific Angles**

**Standard Identities of Trigonometry**

An equation including trigonometric ratios of an angle is called trigonometric identity, if it is true for all values of the angles involved. Standard identities involving a right angled triangles are, for ΔABC

**Example if cos θ + sec θ = 2, the value of cos ^{6}**

**θ+sec**

^{6}θ is SSC (10 + 2) 2012(a) 1

(b) 2

(c) 4

(d) 8

**Example The value of sin ^{2} 5° + sin^{2} 10°+ sin^{2} 15° +… +sin^{2} 85° + sin^{2} 90° is SSC (10 +2) 2012**

(a)7 1/2

(b)8 1/2

(c)10 1/2

(d)9 1/2

**Rules for the Sign of Trigonometric Ratios**

From, the figure given here, we can state the signs for different Trigonometric ratios i.e., If the angle is in

1st quadrant => All trigonometric ratios are positive

IInd quadrant => Only sin and cosec are positive

IIIrd quadrant => Only tan and cot are positive

IVth quadrant => Only cos and sec are positive

**Example If cos θ cosec 23° = 1, then value of θ is SSC (10 + 2) 2012**

(a) 23°

(b) 37°

(c) 63°

(d) 67°

**Reference Corner**

**1. If tan 330° = x, then the value of x. is SSC (10+2) 2017**

(a) -1√3

(b)-√3

(c) -1/2

(d)-1√2

**2. The value of the following is**

**(sin 47°/cos 43°)²+(cos 43°/sin 47°)² – 4cos²45° SSC (10 + 2) 2015**

(a)-1

(b)0

(c)1/2

(d) 1

**3. If tan(A + B) = √3 and tan(A – B) =1/√3 ∠(A + B) < 90°, A ≥ B, then ∠A is SSC (10+2) 2014**

(a) 45°

(b) 60°

(c) 90°

(d) 30°

**4. The value of g is equal to sinθ-2sin³θ/2cos³θ-cosθ is equal to SSC (10+2) 2014**

(a)tanθ

(b)cotθ

(c)sinθ

(d)cosθ

**5. If r sinθ = 7/2 and rcosθ =7√3/2 , then the value of r is SSC (10 + 2) 2014**

(a) 5

(b) 7

(c) 4

(d) 3

**6. If θ + Φ = π/2 and sinθ = 1/2, then the value of sin Φ is**

(a)1/2

(b)√3/2

(c) 1

(d)1/√2

**7. If θ is a positive acute angle and 4cos²θ – 4 cosθ + 1 = 0, then the value of tan (θ – 15°) is equal to SSC (10+2) 2014**

(a) 0

(b) 1

(c) √3

(d) 1/√3

**8. The value of sin25°cos65°+cos25°sin55°/tan²70°-cosec²20° is SSC (10 + 2) 2014**

(a) -1

(b) 0

(c) 1

(d) 2

**9. The product cos 1° cos 2° cos 3° cos 4° … cos 100° is equal to SSC (10 + 2) 2013**

(a)1

(b)0

(c)-1

(d)1/4

**Practice Exercise**

**Answers**

**Hints & Solutions**

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