Introduction to Trigonometry — Notes
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01
8.1 Trigonometric Ratios
For an acute angle θ in a right triangle:
sin θ = perpendicular/hypotenuse
cos θ = base/hypotenuse
tan θ = perpendicular/base
and their reciprocals are cosec θ, sec θ and cot θ.
sin θ = perpendicular/hypotenuse
cos θ = base/hypotenuse
tan θ = perpendicular/base
and their reciprocals are cosec θ, sec θ and cot θ.
02
8.2 Reciprocal Relations
sin θ·cosec θ=1, cos θ·sec θ=1, tan θ·cot θ=1.
03
8.3 Standard Values
Know the values of sin, cos and tan for 0°, 30°, 45°, 60°, 90°.
Memory pattern
sin 0°,30°,45°,60°,90° = √0/2, √1/2, √2/2, √3/2, √4/2.
Cosine values appear in reverse order.
Cosine values appear in reverse order.
04
8.4 Trigonometric Identities
Core identities:
sin2θ + cos2θ = 1
1 + tan2θ = sec2θ
1 + cot2θ = cosec2θ.
sin2θ + cos2θ = 1
1 + tan2θ = sec2θ
1 + cot2θ = cosec2θ.
05
8.5 Complementary Angles
For acute θ:
sin(90°−θ)=cos θ, cos(90°−θ)=sin θ, tan(90°−θ)=cot θ, with corresponding reciprocal relations.
sin(90°−θ)=cos θ, cos(90°−θ)=sin θ, tan(90°−θ)=cot θ, with corresponding reciprocal relations.
⚡ Quick Revision
- SOH-CAH-TOA for sin, cos, tan.
- Learn the five standard angles.
- Three fundamental identities are essential.
- Complementary angles interchange sin↔cos and tan↔cot.
🎯 Board Exam Focus
- Keep the ratio definitions linked to opposite/adjacent/hypotenuse.
- When proving identities, simplify one side at a time.
- Do not assume tan 90° is defined.
🚀 Last-Minute Revision
✔ Read every formula with its conditions and symbols.
✔ Write given data first and keep units consistent.
✔ For proofs, state the theorem and show logical steps.
✔ Check signs, substitutions and final units.
❤️ Examisthan.com • Class 10 CBSE Mathematics • Chapter 8: Introduction to Trigonometry
