radians

when can you use small angle approx?

only when the angle is small, < 10°, and is measured in radians

when is the small angle approximation valid?

only when the angle is small, < 10°, and is measured in radians

what size constitutes as a small angle?

< 10°

what is small angle approx measured in?

radians

sin θ = ?

sin θ = θ

cos θ = ?

cos θ = 1 - θ² / 2

tan θ = ?

tan θ = θ

which small angle approx is the outlier?

cos θ, because cos θ = 1 - θ² / 2

GRAPHS

what symbol should you use in small angle approx?

~ as an equals sign

what should your answer be?

an integer with no thetas

2sinθ = ?

sin2θ = ?

they both equal 2θ

4cosθ = ?

cos4θ = ?

4cosθ = 4(1 - θ² / 2)

cos4θ = 1 - (4θ²) / 2

how do you find the approximate value?

1. find the approximation

2. any theta or theta squared terms (or to the power of whatever) will also be small if theta is small, therefore they can be ignored

3. the approximation is whatever the final non-theta term is