How to Use Trigonometry to Find an Angle

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In order to use trigonometry to find an angle, you really need a strong knowledge of the inverse trig functions at play. Use trigonometry to find an angle with help from a mathematics educator in this free video clip.

Part of the Video Series: Trigonometry Education
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Video Transcript

Hi, I'm Jimmy Chang, and we're here to talk about how to use trigonometry to find an angle. Now, finding an angle is going to be a very important part that you'll have to think about in trigonometry because not only are you supposed to measure the lengths of sides in a triangle or the radius of a circle, you also need to find out what the measurements of the angles are. So in order to use trigonometry to find an angle, what you want to think about is really strong knowledge of the inverse trig functions, specifically the arc sign, arc cosine, arc tangent, just to name a few. Now, arc sine arc cosine and arc tangent also have these kinds of notations, sine inverse, cosine inverse and tan inverse. So these are equal to each other. Now here's just a brief illustration as to how this works. You know for example the tangent theta definition is just as an example Y over X. Now to solve for the angles themselves what you want to do is you want to take the inverse tangent of both sides, not multiplying but finding the tangent, take the tangent inverse of both sides like this and what this tells you here is the tangent inverse and tan they cancel each other out so you have theta is equal to the inverse tangent of Y over X. Now, for example, if you wanted to find what that is, this is where a calculator becomes very handy because suppose if Y was 4 and X was 3, what you'll want to do is on your calculator and make sure that it's in the proper mode here, literally enter tang inverse of 4/3 and that will give you what the angle happens to be. Now more often than not there's going to be more than one right answer so what you want to think about after finding the inverse tan of this is using reference angles to think about what the other quadrants are going to be because the calculator is only going to give you one answer so it's up to you to find out if possible what the other answers might be. But the bottom line is knowledge and comfortability with the inverse trig functions will take you a long way. So I'm Jimmy Chang and that's how to use trigonometry to find an angle.


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