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Is the following statement possible or impossible?
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Sin 𝜃 is equal to 1.2.
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Well, to help us consider this, what we’re going to do is look at a graph of the sine function.
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So what I’ve drawn here is the graph 𝑦 equals sin 𝜃.
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There’re some key things that we can see here.
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Well, first of all, we can see that the maximum and minimum points have 𝑦-coordinates of one and negative one, respectively.
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And we can also see that the period of the graph is 360 degrees.
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And that means that the time it takes to repeat its shape, so do one complete cycle of its shape, is going to be 360 degrees.
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And I’ve marked this in blue.
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Well, for this question, it’s this maximum point that we’re interested in because we’re asked to see whether the statement sin 𝜃 equals 1.2 is possible or impossible.
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Well, this would mean that sin 𝜃 would have to have a 𝑦-value of 1.2.
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Well, as we can see, the maximum 𝑦-value possible for a sine graph is one.
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So therefore, we can say that sin 𝜃 is equal to 1.2 is impossible.
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And that’s because 1.2 is greater than one.