Class notes physics for 11th grade.

SOME IMPORTANT TRIGONOMETRY FORMULAS
sin(x ± y) = sin x cos y ± cos x sin y




cos(x ± y) = cos x cos y ∓ sin x sin y




Double Angle Formulas
• sin 2θ = 2 sin θ cos θ

• cos 2θ = 2 cos2θ - 1

• cos 2θ = 1 - 2 sin2θ

• cos 2θ = cos2θ - sin2θ


Trigonometric Approximation
Example:
cos θ = B / H = 1 ⇒ cos θ ≈ 1




(When θ is very, very small)

• Hypotenuse ≈ Base

• θ is very, very small.



Hypotenuse (H)
θ
Base (B)




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, APPROXIMATIONS & KEY VALUES

Small Angle Approximations
• sin θ ≈ θ

• tan θ ≈ θ


Binomial Approximation
Formula:
(1 + x)n ≈ (1 + nx) when x ≪ 1




Example Evaluation:

Evaluate (1 + 0.00001)10:

• Here, x = 0.00001 which is ≪ 1, and n = 10.

• ⇒ (1 + 0.00001)10 ≈ 1 + (0.00001 × 10)

• ⇒ 1 + 0.0001

• ⇒ 1.0001


Trigonometric Key Values & Thresholds

Trigonometric Ratio Value Condition / Nature

sin 0° 0 Minimum positive quadrant start

sin 90° 1 sin θ reaches its Maximum when θ = 90°

sin 180° 0 Zero-crossing

sin 270° -1 sin θ reaches its Minimum when θ = 270°




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