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
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Exam Patterns
What examiners ask — read before attempting PYQs
✏️Worked Example 2
1
Replace cosec θ = 1/sin θ and sec θ = 1/cos θ
2
(sin θ × 1/sin θ) + (cos θ × 1/cos θ)
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.
Common Mistake #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.