Finding values of all six trig functions right triangle
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do they still welcome to math go to serve.com and this clip we're going to be going over how to find the values of all six trig ratios on a right triangle Let's assume that sweet given this right triangle this is the 90-degree angle here and we have this is Uncle data and instructions are for us to find the value find the values of all six trig ratios for the specified angle okay for the specified angle all right so first things first let's see we have this angle Theta as a given angle and the hypotenuse 13 is provided in this site is also provided S5 not with this triangle first in will want to do is 1 - label the triangle to label the triangle we are going to have to identify the opposite hypotenuse and adjacent why do we want to do that well because we're going to be using this mnemonic tool cold sohcahtoa they help us to determine 3 shows all six trig ratios with reference to this angle right here okay so this is Uncle Theta the given angle then the side opposite the angle is going to be cold you're what your opposite okay other than 90 degree angle is the longest side of the triangle the longest side of a triangle is also known as a hypothesis the other side the third side is your adjacent now these three sides tell us the names that was given the three sides tells us what a h and O and sohcahtoa are okay so we have a beer and we have page those are at the adjacent opposite and hypotenuse of a right triangle with your friends to a specific angle okay so are we going to be size to basically determine the values of all six trig ratios with reference to angle ThetaNow in order for us to find all six trig ratios we need to have the measures of all three sides if you take a look at the triangle that we have here we know where the hypotenuse is we know where the add Jason is both be missing the Opposites okay do we need to determine what it the opposite is before we can proceed so what we're going to do now is you're going to proceed to find the opposite okay to find the opposite We're going to find the Opposites we're going to be in the formula here will be using the advanced version of the Pythagorean theorem to the formulas going to be a square + b square + C Square okay so we have a square + b square + I'm in a skirt plus b squared equals c squared now if you want to adapt the Pythagorean theorem to a triangle of this nature we can simply Express this as the adjacent square plus the opposite Square equals to the hype on the square all right it doesn't matter what you call it be okay if you want to call or adjacent and then be is going to be our opposite and then she will be the hypotenuse all right so we're going to use this formula to determine the missing side which is the opposite so let's go ahead and substitute or adjacent is 5 so we have 5 square plus our opposites we don't know what that is opposite square is equal to your hyperness which is 13 Square that when you simplify 5 square is 25 + the opposite square is going to be 13 Square which is 169 now when you subtract 25 from both sides has go ahead and do that subtract 25 from both sides that will give us opposite square equals 169 - 25 is 144 now go ahead and take the square root of both sides of our equation square root and a square root and that will give us what's the opposite is so they are closed it is going to be 12 now that we have all three sides we can go ahead and I'm so the problem okay so that's partition I work space down the center left list what we have we know that the adjacent is 5 the opposite is 12 and the hypotenuse is 13 all right so let's go ahead and start using sohcahtoa the formula that we had earlier here the acronym to help us determine what sine cosine tangent or and their reciprocals okay let's start with sine sine Theta from so is opposite over hypotenuse so the opposite is 12 and hypothesis 13 so sine Theta is 12 / 13 now the reciprocal of sine is cosecant written a CSC and that we can determine by reciprocating 12 / 13 when you reciprocate 12 over 13 years simply interchange in the numerator and the denominator so that gives you cosecant now cosine Theta we're not going to use the component of sohcahtoa can simply means that cosine is equal to the adjacent divided by the hypotenuse now the adjacent is 5 and hypotenuse is 13 we can use the cosine to find another trig ratio the treat function that's related to co-sign the reciprocation is the secant function okay secant is a reciprocal of cosine so it's simply going to be 13 over 5 the results we get the reciprocating cosine now let's go ahead and find out the last two tan to find to find tan beta we're going to use TOA in sohcahtoa okay