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SBI PO Basic Trig Ratios

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This page covers SBI PO Basic Trig Ratios with complete concept notes, 6 graded practice MCQs, key points and exam-specific tips. Free to study.

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Concept Notes

Basic Trig Ratios— Rules & Concept

Core ConceptRead this first — the foundation of the topic
Core Concept

In a right triangle, trigonometric ratios connect an angle with the ratios of two sides. For any angle θ (theta), there are six basic ratios: sine, cosine, tangent, cosecant, secant, and cotangent

Key Definitions

Consider a right triangle with angle θ. The three sides are: Hypotenuse (longest side, opposite to 90°), Opposite (side facing angle θ), and Adjacent (side next to angle θ)

Basic Ratios

sin θ = Opposite/Hypotenuse cos θ = Adjacent/Hypotenuse tan θ = Opposite/Adjacent cosec θ = 1/sin θ = Hypotenuse/Opposite sec θ = 1/cos θ = Hypotenuse/Adjacent cot θ = 1/tan θ = Adjacent/Opposite Fundamental Identity: sin²θ + cos²θ = 1 (Most important for SSC CGL) Other Identities: 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ

Exam PatternsWhat examiners ask — read before attempting PYQs

SSC CGL asks direct ratio calculations, value finding, and identity-based problems. Questions often involve standard angles (0°, 30°, 45°, 60°, 90°) and basic identities. Shortcut #1 - Standard Angle Values: For 0°, 30°, 45°, 60°, 90°: sin values: 0, 1/2, 1/√2, √3/2, 1 cos values: 1, √3/2, 1/√2, 1/2, 0 tan values: 0, 1/√3, 1, √3, undefined Memory trick: sin 30° = 1/2, sin 60° = √3/2 (opposite values for cos)

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Use identity sin²θ + cos²θ = 1

2
Step 2

(3/5)² + cos²θ = 1

3
Step 3

9/25 + cos²θ = 1

4
Step 4

cos²θ = 1 - 9/25 = 16/25

5
Step 5

cos θ = 4/5 (taking positive value)

6
Step 6

tan θ = sin θ/cos θ = (3/5)/(4/5) = 3/4 Answer: cos θ = 4/5, tan θ = 3/4 Shortcut #2 - Quick Identity Check: Whenever given one ratio, immediately use sin²θ + cos²θ = 1 to find others. This saves calculation time in exams. Worked Example 2: Simplify (sin θ × cosec θ) + (cos θ × sec θ)

1
Step 1

Replace cosec θ = 1/sin θ and sec θ = 1/cos θ

2
Step 2

(sin θ × 1/sin θ) + (cos θ × 1/cos θ)

3
Step 3

1 + 1 = 2 Answer: 2 Shortcut #3 - Reciprocal Recognition: Instantly recognize reciprocal pairs: sin-cosec, cos-sec, tan-cot. Their product always equals 1.

Exam TrapsCommon mistakes students make — avoid these

#1: Students often confuse opposite and adjacent sides when angle position changes. Always identify the angle first, then mark opposite and adjacent accordingly. Many students lose marks by mixing up sin and cos definitions when the triangle orientation changes.

Practice identifying sides relative to the given angle, not the triangle's position on paper. Practical Exam Tip: In multiple choice questions, if you get values like sin θ = 4/3 or cos θ = 6/5, immediately mark it wrong. Sine and cosine values cannot exceed 1. This elimination technique saves precious exam time.

Key Points to Remember

  • sin θ = Opposite/Hypotenuse, cos θ = Adjacent/Hypotenuse, tan θ = Opposite/Adjacent
  • cosec θ, sec θ, cot θ are reciprocals of sin θ, cos θ, tan θ respectively
  • Fundamental identity: sin²θ + cos²θ = 1 (appears in 80% of trigonometry questions)
  • Standard angles: sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2
  • cos 30° = √3/2, cos 45° = 1/√2, cos 60° = 1/2
  • tan 30° = 1/√3, tan 45° = 1, tan 60° = √3
  • Quick check: sin θ and cos θ values must always be between -1 and 1
  • Identity shortcut: 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ
  • Reciprocal product rule: sin θ × cosec θ = 1, cos θ × sec θ = 1, tan θ × cot θ = 1
  • Always identify opposite and adjacent sides relative to the given angle, not triangle position

Exam-Specific Tips

  • sin 30° = 1/2 and cos 60° = 1/2 (complementary angles have equal values)
  • sin 45° = cos 45° = 1/√2 = √2/2
  • tan 45° = 1 (only standard angle where tangent equals 1)
  • sin 0° = 0, cos 0° = 1, tan 0° = 0
  • sin 90° = 1, cos 90° = 0, tan 90° is undefined
  • √2 ≈ 1.414 and √3 ≈ 1.732 for decimal calculations
  • In any right triangle, hypotenuse is always the longest side
  • Maximum value of sin θ or cos θ is 1, minimum value is -1
Practice MCQs

Basic Trig Ratios — Practice Questions

6graded MCQs · easy to hard · full solution & trap analysis

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Practice 1medium

A ladder leans against a wall such that it makes an angle of 60° with the ground. If the ladder is 10 metres long, find the height at which the top of the ladder touches the wall (in metres).

Practice 2hard

If sin θ = 3/5 and θ lies in the second quadrant, find the value of (5 tan θ + 4 sec θ).

Practice 3hard

Given that tan α = 1/2 and tan β = 1/3, where α and β are acute angles, find sin(α + β).

Practice 4hard

A ladder leans against a wall such that it makes an angle of 60° with the ground. If the ladder is 10 metres long, find the height at which the ladder touches the wall (in metres).

Practice 5hard

If sin θ + cos θ = √2, find the value of sin θ cos θ.

Practice 6hard

If 3 sin θ + 4 cos θ = 5, find the value of tan θ.

60-Second Revision — Basic Trig Ratios

  • Remember: sin²θ + cos²θ = 1 is the most tested identity
  • Formula: Standard angles - sin 30°=1/2, sin 60°=√3/2, sin 45°=1/√2
  • Trap: Never accept sin θ or cos θ values greater than 1 in any answer choice
  • Quick tip: cosec, sec, cot are just reciprocals - flip the fraction
  • Check: Opposite side is always relative to the given angle, not triangle orientation
  • Speed trick: Use complementary angle property - sin θ = cos(90°-θ)
  • Final check: In MCQs, eliminate impossible ratio values first
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