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