Final answer:
The formula for measuring angular distance in small angles can be taken as the angle itself in radians, as sine and tangent of the angle for small angles approximate the angle in radians.
Step-by-step explanation:
The formula for measuring angular distance in small angles is often taken to be the angle itself when measured in radians. This is because for small angles, the values of sine and tangent of the angle approximate the angle in radians. A circle consists of 360 degrees, so if you need to represent a small angle θ in radians and compare it to degrees, you could use the approximation θ radians = θ in degrees x (π/180), where π (pi) is approximately 3.14159.
options given (a) Sinθ, (b) Tanθ, (c) θ/180, and (d) θ/360 don’t directly provide a formula for small angles. However, option (c) θ/180 is a part of the conversion factor from degrees to radians, which is closely related to measuring angular distances in radians.
For example, to convert 1 degree to radians, we use 1° x (π/180) = 0.01745 radians, which shows that 1 radian is approximately 57.3° as given in option a. of an ancillary question. This is also relevant when considering the angle of rotation and angular velocity.