#checking if a point is in an angle of a sphere

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final nest
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Hello. English is not my main language that's why it could be hard to translate mathematic vocabulary into english so please tell me if I tell anything wrong.
so my problem is that I have a sphere with a radius of 4 metres and I have to check whether a point is in the sphere in a specific angle.
I added a picture of the sphere and the angle which is marked as a black line.
I already tried to find out how to check whether a point is in that angle but I wasn't successful.
I hope someone here is able to help me.
I'm still going to school that's why I may not understand VERY complicated answers.
Best greetings.

solemn sunBOT
final nest
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checking if a 3d point is in a globes angle

final nest
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checking if a point is in an angle of a globe

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checking if a point is in an angle of a sphere

pine citrus
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