INSTRUCTOR: --video you learned how to use the unit circle to evaluate functions like sine of 60 degrees, which is the same thing as sine of pi/3. So on the unit circle, when we make an angle turn of 60 degrees, which is the same thing as pi/3 radians, we see that sine of 60 degrees is the same thing as the square root of 3 over 2. 

We can do the same thing with the second example. If I want to know what is cosine of 240 degrees, I can go to the unit circle and search for an angle turn of 240 degrees. That puts me in the third quadrant here. And we can see that at 240 degrees, cosine is the x-coordinate. So that's the negative 1/2. But we also know that an angle turn of 240 degrees is the same thing as 4 pi over 3 radians. So again, cosine of 4 pi over 3 radians is still negative 1/2. 

So the unit circle gives us exact values, exact values meaning square root of 3 over 2, not an approximate value, which would be a decimal. But you can actually use your calculator to get approximate estimations as well. So on your calculator, we can find sine of 60 degrees. But before we put in the input value of 60 degrees, you have to make sure that your calculator is in degree mode. So any time you take sine, cosine, or tangent of a degree term, you have to go to Mode. 

And here, scroll down. And right now, your calculator has probably defaulted to radian mode. You just want to switch it over to degree mode. So when I switch over to degree mode-- I'm going to press 2nd Quit here. So I'm going to quit out of that. I can type in sine of 60. And now my calculator knows that that is 60 degrees, not 60 radians, because that's not the same thing. Notice that you get 0.866, which is the same thing as the square root of 3 divided by-- oops. Let me try that again-- square root of 3 divided by 2. 

OK. So this is how you can use the calculator to get approximate values of sine and cosine. We can also check out cosine of 240 degrees. So again, right now, my calculator is in degree mode. So I can go ahead and take cosine of 240 degrees. And you'll see it's going to give you negative 1/2. OK. Now, what if you want to take sine of pi over 3? Now, if your calculator is in degree mode, you will not get 0.866. 

So again, right now, my mode is in degree mode. I'm going to just show you what happens if my calculator's not in the correct mode. So if I take sine of pi, divide it by 3, because this value, pi/3, is not degrees, it's in radians, notice when I press Enter, I don't get 0.866. OK? So I get a different answer. And it's not the correct answer. 

So any time you're taking sine, cosine, or tangent of a radian measurement, you have to make sure you switch the mode back to radian mode. OK. So if I switch back to radian mode here, let's repeat sine of pi over 3-- so sine of pi divided by 3. You'll see that this is now the same as sine of 60 degrees, so 0.866. 

Again, let's try cosine of 4 pi over 3. So cosine of 4 pi over 3 should be the same thing as cosine of 240 degrees. So we know the answer should be negative 1/2. Now, check. Make sure that you're in radian mode. So I am in radian mode. So if I take cosine of 4 pi over 3-- so 4 pi over 3 is in radians. Notice that it will give you the same solution as cosine of 240 degrees. So we get negative 0.5. 

So this is how you can use your calculator function. The reason why I'm showing you how to use your calculator function is because we also know that sometimes when we look at certain functions, the function's amplitude is not always going to be 1. So for example, here, sine of 60 degrees, the amplitude of this sine function is 1, which means that we're on the unit circle. The same thing with cosine of 240 degrees-- the amplitude of this cosine function is also 1, which means we're on the unit circle. 

But what happens when we're looking at functions like the Ferris wheel problem, where for the Ferris wheel problem, the amplitude is not 1? So we're not on the unit circle anymore. Now we're looking at a Ferris wheel, so a circle that's much larger than the unit circle. And the amplitude now is 225b. So 225 is much larger than 1. How can we calculate sine and cosine of specific values on, let's say, the Ferris wheel problem when the amplitude is not 1? So I'll show you that next in the next video.