For very small angles, you can approximate values for the sine, cosine, or tangent. This is useful when calculating the fringe separations in interference patterns.
When θ is measured in radians, a small angle segment approximates to s/r where s is the arc length and r is the radius. In other words, for a small angle segment, we can write, θ = s/r.
The rules for Small Angle Approximations are:
sin θ ≈ tan θ ≈ θ
cos θ ≈ 1
To convert the angle in radians into an angle in degrees, remember that one radian is 180/π ≈ 57.3 degrees.
Exercise:
Use the small-angle rule to write down these values:
a) tan 0.01 radians
b) cos 0.05 radians
c) sin 0.03 radians.
