Trigonometry Questions for SSC CGL
School-level trigonometry. Almost every question falls to a few facts.
Trigonometry in SSC CGL is school-level: the six ratios, a handful of standard values, three identities, complementary angles, and simple heights and distances. The Tier 2 syllabus itself says heights and distances are "simple problems only".
That makes it one of the most scoring maths chapters. Almost every question falls to one of the facts below. Learn them until you do not have to think, then practise the question types at the end.
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Standard Values
The one table to know by heart. "Not defined" means the value does not exist.
sin θ
0°
0
30°
1/2
45°
1/√2
60°
√3/2
90°
1
cos θ
0°
1
30°
√3/2
45°
1/√2
60°
1/2
90°
0
tan θ
0°
0
30°
1/√3
45°
1
60°
√3
90°
Not defined
| Ratio | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin θ | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| tan θ | 0 | 1/√3 | 1 | √3 | Not defined |
Ratios, Identities and Complementary Angles
- The three base ratios
- In a right triangle: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent.
- Reciprocals
- cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ.
- Three identities
- sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.
- Complementary angles
- Two angles that add to 90°. sin(90° − θ) = cos θ, tan(90° − θ) = cot θ, sec(90° − θ) = cosec θ.
- Degrees and radians
- 180° = π radians. To convert degrees to radians, multiply by π/180.
- Angle of elevation
- The angle you look up from the horizontal to see the top of an object. Angle of depression is the angle you look down.
Worked Practice Questions
Original practice questions, not taken from any past paper.
- 1
Practice question 1: If sin θ = 3/5 and θ is acute, find tan θ.
Opposite = 3, hypotenuse = 5, so adjacent = √(25 − 9) = 4. tan θ = opposite ÷ adjacent = 3/4.
- 2
Practice question 2: Find sin²30° + cos²60°.
sin 30° = 1/2 and cos 60° = 1/2. So (1/2)² + (1/2)² = 1/4 + 1/4 = 1/2. Note that this is not sin²θ + cos²θ = 1: the two angles are different.
- 3
Practice question 3: Find sin 37° ÷ cos 53°.
37° + 53° = 90°, so sin 37° = cos(90° − 37°) = cos 53°. The ratio is 1. Any question with odd angles like 37° and 53° is usually a complementary angle question.
- 4
Practice question 4: Simplify (1 + tan²θ) × cos²θ.
1 + tan²θ = sec²θ, and sec²θ × cos²θ = 1. Answer: 1.
- 5
Practice question 5: If sec θ + tan θ = 3, find sec θ − tan θ.
sec²θ − tan²θ = 1, so (sec θ + tan θ)(sec θ − tan θ) = 1. sec θ − tan θ = 1/3. Check: adding gives 2 sec θ = 10/3, so sec θ = 5/3 and tan θ = 4/3; then 25/9 − 16/9 = 1.
- 6
Practice question 6: Convert 135° to radians.
135 × π/180 = 3π/4 radians.
- 7
Practice question 7 (heights and distances): A pole casts a shadow 20√3 m long when the sun's elevation is 30°. Find its height.
tan 30° = height ÷ shadow, so height = 20√3 × 1/√3 = 20 m. Use tan because the height and the shadow are the two sides next to the right angle.
- 8
Practice question 8 (heights and distances): A 10 m ladder leans on a wall, making 60° with the ground. How far is its foot from the wall, and how high does it reach?
The ladder is the hypotenuse. Foot distance = 10 × cos 60° = 5 m. Height = 10 × sin 60° = 5√3 m, about 8.66 m.
Data interpretation and arithmetic in the exam style. No signup.
How SSC Tests Trigonometry, and the Traps
Three question types cover most of this chapter: find a value from given information (questions 1 and 5), simplify an expression with identities or complementary angles (questions 2 to 4), and heights and distances (questions 7 and 8).
The traps are small. Using sin where tan is needed in a shadow problem. Reading sin²30° + cos²60° as an identity. Mixing up sin 60° and cos 60°. A quick check that saves marks: sin and cos are never greater than 1, so an answer above 1 for either is wrong.
Before You Sit the Paper
- checkWrite the values table from memory in under a minute
- checkKnow all three identities and the forms they take when rearranged
- checkSpot complementary pairs instantly: angles that add to 90°
- checkDraw a rough figure for every heights and distances question
- checkPractise timed sets; Tier 1 gives about 36 seconds per maths question
FAQs
Which trigonometry topics are in the SSC CGL syllabus?expand_more
Trigonometric ratios, degree and radian measures, standard identities, complementary angles, and heights and distances. Tier 2 says heights and distances are simple problems only.
Is trigonometry hard in SSC CGL?expand_more
No. SSC sets Tier 1 maths at 10th standard level, and most questions fall to the values table, three identities and complementary angles.
What is the trick for trigonometry questions in SSC?expand_more
Look for complementary angles (pairs adding to 90°) and for identities like sec²θ − tan²θ = 1. Many long-looking expressions reduce to 0 or 1.
How do I solve heights and distances questions?expand_more
Draw a right triangle, mark the angle of elevation or depression, and use tan when the two known or wanted sides are the ones next to the right angle. Use sin or cos when the slanted side is involved.
Next steps
Take a full SSC CGL mock testThe whole Tier 1 syllabus in one timed, scored paper.