Hi, thank you very much for this website, I have been finding it very useful in my preparations for the PAT.
Could you possibly explain why sinθ < 1?
It’s a pleasure — I’m glad it’s been useful. Actually this is a mistake: the answer should say sin x <= 1. This is just a consequence of the fact that for all real angles, the value of sin x varies between -1 and +1.
The question below does point out that sin x can be greater than 1 if x is a complex number. But in general in the PAT exam I think you should treat variables as real numbers unless they are explicitly stated to be complex.
Never does it state that theta must be a real number though. Or are complex numbers just not on the PAT syllabus?
It’s true that sin x can be greater than 1 for complex x, but in general I think the assumption is that we are talking about real numbers and -1 <= sin x <= 1. In general I think that you are better off treating variables as real unless it’s stated in the question that they are complex.
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