Video: Pack 4 • Paper 3 • Question 2

Pack 4 • Paper 3 • Question 2


Video Transcript

Use your calculator to work out sin 20 degrees over tan 20 degrees all squared minus the square root of cos 35 degrees. Part a) Write down all the figures shown on your calculator’s display. Part b) Write your answer to part a accurate to three significant figures.

So part a is actually quite self-explanatory. You’re just gonna put this calculation into your calculator. However, I just wanna bring your attention to a couple of common errors that people can make when they’re doing this kind of question.

The first thing to actually know is that actually when you’ve got your calculator, you have a little display at the top. And in the display in your calculator, you should have somewhere display probably along the top of the main display a d, a capital D, a Deg, something along these lines that basically tells you that your calculator is actually calculating in degrees. Because if we look in the question, all our angles, so the sin of 20, the tan of 20 and the cos of 35, are all in degrees. And if we don’t have this, if we don’t have it in this mode, we’re not calculating in degrees, then we’ll actually find we’re gonna get a wrong answer and this is very common. So make sure before you start that your calculator is in the correct mode. And this brings us to another point: make sure you know your calculator, so you know how to change it into the correct mode if you’re in an exam or a situation where you have to use it.

The next key point is just remember to make sure that you use brackets because we want to make sure that we’re actually squaring sin 20 degrees divided by tan 20 degrees, not just squaring one of the terms individually. And the final tip is that if you actually get an answer, maybe not with this question, but a question like it, you get an answer that actually comes across in a fraction or a surd and actually you’re looking to actually give it in decimals, then you might have a button like this, which is an SD button, and you can actually press this button and it will actually change between the modes. So actually, you’ll finally get it to a decimal answer, which is what you require for a question like this.

So therefore, we move on to the actual answer for part a. So if we’re gonna write down all the figures shown on our calculator’s display when we actually calculate sin 20 degrees divided by tan 20 degrees all squared minus the square root of cos 35 degrees, well, it’s gonna be equal to negative 0.02204796593.

Okay, so we now can move on to part b. Well, we can see in part b that we actually want the answer for part a accurate to three significant figures. Well, again, I’m just gonna draw your attention to a common mistake. And this common mistake is that often people got “Okay, three significant figures. So we go right, we got 0.02. So therefore, that two, that I’ve underlined there, is gonna be our third significant figure.” But no, this isn’t the case.

And the reason why it’s not the case is because actually we disregard any zeros that are actually before our first nonzero digit. So therefore, in fact, our third significant figure would be this zero because we’ve got negative 0.0. So we disregard those two zeros. Then, two will be our first significant figure, the next two will be our second significant figure, and this zero would be our third significant figure.

So now, what we do is we actually look at the number to the right of our significant figures, so our third significant figure in this case. And we could see that we’ve got a four. And because this four is actually less than five, then it means that our zero is just gonna stay the same. So it’s gonna stay as zero. If it was five or greater, then our zero would actually round up, so turn into a one.

So therefore, we can say that sin 20 degrees divided by tan 20 degrees all squared minus the square root of cos 35 degrees is equal to negative 0.0220 to three significant figures. And remember we leave the zero on the end because actually that helps us to note that we’ve actually rounded to three significant figures.

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