Physics Question: If sin(theta)=theta, what does cos(theta)= ? too?

Question

If sin(theta)=theta, what does cos(theta)= ? too? (for small angular aproximation)

Answer 1

sin(θ) ≈ θ
So cos (θ) ≈ 1 because cos (0) = 1
More accurately cos (θ) ≈ 1 - θ²/2

Answer 2

The power series for sin has all odd power terms beginning with x

sin x = x + x^3/3! + x^5/5! + ....

cos has only even powers starting with x^0 = 1:
cos x = 1 + x^2/2! + ...

Thus for very small values of x you can use just the first term as the approximation...

Consider how angles in radians are defined. Compare it to angles on a unit circle. You can see clearly the validity of the approx.

This is a fairly standard way to deal with small values....

Answer 3

1

if sin(θ) = θ then θ = 0
cos(0) = 1

if sin(θ) = x,
cos(θ) = √(1-x²)
works for any value of x, not just small ones.

Answer 4

1/cosC=secC<<<>>>