Trigonometry + Derivatives + Taylor Series

PHYSICS 1 - CHAPTER 0_MATH REVIEW

sin (π - θ) = ?

sin θ

cos (π - θ) = ?

- cos θ

sin (π/2 - θ) = ?

cos θ

cos (π/2 - θ) = ?

sin θ

sin (θ + π/2) = ?

cos θ

cos (θ + π/2) = ?

- sin θ

sin (π + θ) = ?

- sin θ

cos (π + θ) = ?

- cos θ

sin (- θ) = ?

- sin θ

cos (- θ) = ?

cos θ

cos²θ + sin²θ = ?

1

tan²θ = ?

1/(cos²θ) - 1

cos (a + b) = ?

cos(a).cos(b) - sin(a).sin(b)

sin (a + b) = ?

sin(a).cos(b) + sin(b).cos(a)

Derivative of tan(x)

1/cos²x

Derivative of 1/xⁿ

-n/xⁿ⁺¹

Taylor Series:

(1+x)ⁿ ≃ ?

1 + nx

Taylor Series:

1/(1+x)ⁿ ≃ ?

1 - nx

Taylor Series:

ln(1+x) ≃ ?

x

Taylor Series:

e^x ≃ ?

1 + x

Taylor Series:

cos(x) ≃ ?

1 - x²/2

Taylor Series:

sin(x) ≃ ?

x

Taylor Series:

tan(x) ≃ ?

x

Taylor Series:

Under what condition do these approximations apply?

for x close to 0 !!!

Infinitesimal variation (df) of a function f?

df = f (x+dx) - f(x)