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Find a positive angle less than 360\deg that is coterminal to 810\deg .

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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°.

User Mpallansch
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