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

Find the smallest negative equivalent of 961°.

02:12

Video Transcript

Find the smallest negative equivalent of 961 degrees.

Before we try and find an equivalent of 961 degrees, it would be worth it to try and find where 961 degrees falls. Starting with an 𝑥- and 𝑦-plane, we can let the initial arm of this angle be at zero degrees. We know that a full rotation is 360 degrees. And so, it can be helpful to find out how many full rotations are in 961 degrees. When we do that division, we get 2.669 with a four repeating. This tells us we’ll get two complete turns.

So, we multiply 360 degrees by two, and get 720 degrees. And then, we take 961 degrees, and we subtract 720 degrees, which is 241 degrees. This means that from the initial arm, we need to go 241 degrees, which gives us our terminal arm. What we’re saying is that 961 degrees is in the same position as 241 degrees. And it means that 241 degrees is an equivalent to 961 degrees.

However, this is not a negative equivalent. This is because we measure angles in a counterclockwise manner. Counterclockwise measurements are positive. And clockwise measurements are negative. And that means to find the smallest negative equivalent to 961 degrees, we’ll need to move clockwise from the initial arm. We know that the counterclockwise measurement is 241 degrees. If we subtract 241 degrees from 360 degrees, we get 119 degrees. But because this angle is moving in the clockwise direction, we should call it negative 119 degrees.

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