Answer:
The positive angle less than 360° that is coterminal to 810° is θ = 10.114159... radians, or approximately 161.6°.
Explanation:
To find a positive angle less than 360° that is coterminal to 810°, we first need to convert 810° to radians using the formula:
θ = 810° * (π/180)
θ = 11.114159... radians
Then, we can simply add or subtract any multiple of 360° (or 2π radians) to this value to get other angles that are coterminal to it:
θ + 360° = 360° + 11.114159... radians = 11.114159... radians
θ + 360° = (2π + 11.114159...) radians = (-1 + 11.114159...) radians
So we can see that a positive angle less than 360° that is coterminal to 810° is:
θ = 11.114159... radians = (-1 + 11.114159...) radians
θ = (2π + 11.114159...) radians = (-1 + 11.114159...) radians
We can rewrite these equations to determine the exact value of θ:
0 + θ = 11.114159...
θ = -1 + 11.114159...
θ = 10.114159... radians
So the positive angle less than 360° that is coterminal to 810° is θ = 10.114159... radians, or approximately 161.6°.