Video: Finding the Measure of the Smallest Negative Angle Equivalent to a Given One

Find the smallest negative equivalent of 300°.


Video Transcript

Find the smallest negative equivalent of 300 degrees.

So when we’re looking at equivalent angles, what we’re looking at is coterminal angles. And these angles are in a standard position. So it means that their initial side is on the positive 𝑥-axis. And they have a common terminal side. So it means that they’re finished in the same place. So we can see that our terminal side is here, shown in pink. And we can see that the angle that we’ve got is 300 degrees.

Now to find the smallest negative equivalent of 300 degrees, what we need to do is subtract 360 degrees because that’s thinking if we started at our terminal side and then we went round 360 to finish our internal side, then this would give us a negative equivalent of negative 60 degrees. And if we were looking for a positive equivalent of 300 degrees, we could’ve added 360. That would’ve taken us to 660. And this would’ve been an equivalent because again it would’ve had a common terminal side because we just started and then finished at the same terminal side.

So we can say that the smallest negative equivalent of 300 degrees is negative 60 degrees.

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