How to Calculate Sin, Cos & Tan With No Calculator

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Calculating Sin, Cos and Tan with no calculator requires you to remember one phrase: SOHCAHTOA. Calculate Sin, Cos and Tan with no calculation with help from an experienced mathematics educator in this free video clip.

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Video Transcript

Hi, my name is Marija, and today I'm gonna show you how to calculate sin, cosin and tangent with no calculator. And you can do this very easily if you can remember the word SOHCAHTOA and what it stands for. So, SOHCAHTOA, the s stands for sin, the c stands for cosin, and the t stands for tangent, and this word is gonna tell you the formulas for all three. So sin is gonna be the opposite over the hypotenuse. Cosin will be the adjacent over the hypotenuse. And tangent will be the opposite over the adjacent. So if you can remember that, then I'm gonna show you how to apply it now. So we have a right triangle, so that we can do trig, and we'll call this angle here theta, and we'll call our side a, b and c. So if we're trying to find let's say the sin of theta, we're looking for the side that is opposite and the hypotenuse. So when I say opposite, I mean you go to theta, and you drag your pencil opposite of the angle, and that means that we end up at a. And the hypotenuse is always the side that's opposite the 90 degree angle, so that means that it is c. So the sin of theta is a over c. So now if you were given values here, if we had a is three and c is five for example. Let's say this was three, and this was five, then we'd say that the sin of theta is three over five, and then if you wanted it as a decimal, you can just put in your calculator or divide, and you found it without using a calculator. For the cosin we're gonna follow the same process. So the cosin of theta, we're gonna go adjacent over hypotenuse. So for adjacent, we're looking for the side that is right next to theta. Now there's two sides right next to theta, there's b and there's c. However, c is our hypotenuse, so it can't be called two different things. So b is our adjacent side. So b will go on the numerator, and c will go in the denominator, and again you'll just divide if you have numerical values. And for tangent of theta, we're gonna go opposite over adjacent. So the opposite is a, and the adjacent is b, and we'll just substitute values in there and divide, and that is how you find all the three trig values without using a calculator.


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