Trigonometric Ratios of Standard Angles

• Define sin θ, cos θ, tan θ in a right triangle.
• Memorise exact values for 0°, 30°, 45°, 60°, 90°.
• Use complementary angle relations: sin(90°−θ) = cos θ.

1. sin θ = opposite/hypotenuse; cos θ = adjacent/hypotenuse; tan θ = opposite/adjacent.
2. Standard table — sin 30° = 1/2, cos 60° = 1/2, tan 45° = 1, sin 90° = 1, cos 90° = 0.
3. Complementary — sin 30° = cos 60°; tan 30° = cot 60°.
4. Undefined — tan 90° and sec 90° are not defined.
5. NCERT — derive values using special triangles (45°-45°-90° and 30°-60°-90°).

Find sin 30°, cos 60°, tan 45° from a 30°-60°-90° triangle

In 30°-60°-90° triangle with hypotenuse 2:
Side opposite 30° = 1, opposite 60° = √3
sin 30° = 1/2, cos 60° = 1/2
tan 45° = 1 (from isosceles right triangle)

• Swapping sin and cos values (sin 60° = √3/2, not 1/2).
• Using degrees/radians mix-up (Class 10 uses degrees).
• Writing tan 90° = 0 (it is undefined).

• Write sin 45°, cos 45°, tan 60°.
• If sin θ = cos θ, what is θ in [0°, 90°]?
• Evaluate sin²30° + cos²30°.

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