SSC CGL Quant – Trigonometry – Level 1 · Warm-up · Tier I Level

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SSC CGL Quant – Trigonometry – Level 1 · Warm-up · Tier I Level – 12 questions, subject: Quantitative Aptitude. Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.

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1.  
If sin θ = 3/5 and θ is acute, then cot θ is:

Correct Answer: C [4/3]

Explanation:

3-4-5 triangle: P = 3, B = 4, H = 5 → cot θ = B/P = 4/3.

2.  
Find the value of tan 45° + sin 30° × cos 60°.

Correct Answer: A [5/4]

Explanation:

1 + ½ × ½ = 1 + ¼ = 5/4.

3.  
225° expressed in radians is:

Correct Answer: D [5π/4]

Explanation:

225 × π/180 = 5π/4.

4.  
2π/3 radians expressed in degrees is:

Correct Answer: B [120°]

Explanation:

2/3 × 180° = 120°.

5.  
The value of sin² 37° + sin² 53° is:

Correct Answer: C [1]

Explanation:

53° = 90° − 37°, so sin 53° = cos 37° → sin² + cos² = 1.

6.  
If tan θ = 1 and θ is acute, then sin θ + cos θ equals:

Correct Answer: D [√2]

Explanation:

θ = 45° → 1/√2 + 1/√2 = 2/√2 = √2.

7.  
Find the value of cosec 30° + sec 60° − cot² 45°.

Correct Answer: A [3]

Explanation:

2 + 2 − 1 = 3.

8.  
If sin (θ + 20°) = cos 40° and θ + 20° is acute, then θ is:

Correct Answer: B [30°]

Explanation:

θ + 20° + 40° = 90° → θ = 30°.

9.  
A pole casts a shadow 10√3 m long when the sun's elevation is 30°. The height of the pole is:

Correct Answer: C [10 m]

Explanation:

h = shadow × tan 30° = 10√3 × 1/√3 = 10 m.

10.  
Statement-basedWhich of the following is/are correct?
I. sin 60° = cos 30°
II. tan 30° × tan 60° = 1

Correct Answer: D [Both I and II]

Explanation:

Both are complementary-angle facts: √3/2 = √3/2 and (1/√3)(√3) = 1.

11.  
Match the following
P. sin 0° Q. cos 0° R. tan 30°
1. 1/√3 2. 0 3. 1

Correct Answer: B [P-2, Q-3, R-1]

Explanation:

sin 0° = 0, cos 0° = 1, tan 30° = 1/√3.

12.  
A 20 m ladder leans against a wall and makes an angle of 60° with the ground. How far is its foot from the wall?

Correct Answer: A [10 m]

Explanation:

Distance = 20 × cos 60° = 10 m.

➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Quantitative Aptitude book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-quantitative-aptitude

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