Question Video: Determining Whether a Value Is in the Range of a Trigonometric Function Mathematics

Is the following statement possible or impossible? sin 𝜃 = 1.2.

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Video Transcript

Is the following statement possible or impossible? Sin 𝜃 is equal to 1.2.

Well, to help us consider this, what we’re going to do is look at a graph of the sine function. So what I’ve drawn here is the graph 𝑦 equals sin 𝜃.

There’re some key things that we can see here. Well, first of all, we can see that the maximum and minimum points have 𝑦-coordinates of one and negative one, respectively. And we can also see that the period of the graph is 360 degrees. 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. And I’ve marked this in blue.

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. Well, this would mean that sin 𝜃 would have to have a 𝑦-value of 1.2. Well, as we can see, the maximum 𝑦-value possible for a sine graph is one.

So therefore, we can say that sin 𝜃 is equal to 1.2 is impossible. And that’s because 1.2 is greater than one.