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Video Notes 8.3 - Geo

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Please correct the mistake on Example #4 of the video. I punched in my numbers incorrectly into the calculator. The angle = 34.82 degrees in example #4. Not 60.254 degrees. Sorry about that.

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hello everybody this is mrs. on Tiana and these are your notes for our next section 8 alright this is geometry for your composition books please write notes 8.3 trig functions or trigonometric functions the topics of women cover today are the signing the cosine independent function so let's get into it all comes from will they come from similar right triangles by angle angle similarity that's the concept we're starting so much special case particularly right triangles that's where this comes from bonding site because when you have similar triangles the corresponding sides are proportional and those should be equal well those races are called trigonometric so that's what we're studying in essence were starting nothing more than a special case of similar triangles in this case then being right triangles here's the goal behind studying trig functions you want to find the missing side lengths of right triangles  memorized following acronym memorize it's going to help you out once use it a couple times you won't have to worry about memorizing what it means let me zoom in for you here okay  is acronym please for a long long time the sine function for the cosine function the T for the tangent function that for opposite the H stands for hypotenuse the a stands for adjacent notice that the cosine function has an adjacent and the hypotenuse the tangent function has an opposite and adjacent Wireless look at these words in terms of the actual function so the sine function is and hypotenuse values or they're using opposite and upon his values this is how we lights I guess this you can call this a notation Behind These functions we shorten the word sign by taking the out this civil right here stands for data the angle you going to type in or write an angle in here and you're going to calculate the ratio on the opposite side from that angle over the the cosine is looking at the adjacent side lengths over the hypotenuse and the tangent function so the tangent what angle Theta is looking at the opposite side over the adjacent side okay now that you've what these functions look like let's go ahead and apply them here we go here's our first example I have an Engel I first will have a right single typical if you want to find find a silent W as in this case you would use the Pythagorean theorem but we can't use the Pythagorean theorem because we don't have tell me enough information we do have this angle measurement 54 degrees so from this vantage point of 54 degrees notice that W is opposite side lengths of angle 5417 so I have an from the vantage point of this angle I have an side and hypotenuse which of these functions utilizes the opposite side and hypotenuse that would be the sine function so this is how you work out the problem using your sign function sine of 54 degrees equals the opposite side which is W over which is 17 now it's important to understand that this point we are going to be using our calculators on makes a scientific calculator so that you can in fact calculate these functions go ahead and calculate what the sign 54 degrees is in rounded to the thousands so I'm going with 0.809 equals W / 17 little bit of algebra go ahead and cross multiply w1s it's all by itself is going to be pointless 809 times 17 equals 13.75 are you there is the side length of course to Susan approximation on an exact measurement let's take a look at a couple other examples  right here's the next one all right from this Vantage Point 20 degrees here I have an opposite side from 20 degrees and an adjacent side consider the hypotenuse and adjacency 228-d hypotenuse is the hypotenuse never consider the hypotenuse and adjacent side to any angle she's inside it's only considered for the legs of the right triangle opposite adjacent what function is that that would be the function and so we're going to go ahead and write the tangent of 28 degrees tangent of 28 degrees equals the opposite which is 1 over the adjacent side which is W it's go ahead and cross multiply here so I have what are you times the tangent of 28 degrees go ahead and punch that into your calculators 28° calculating the tangent rounded to the thousand 0.532 equals 1 go and solve for w by dividing both sides W going to be up doximity 1 divided by 0.532 equals .87 nights at 1.88 is your final answer here to take a look at third exam this vantage point I have at 33 degrees I'm looking at. Knees I'm looking at an adjacent angle adjacent and what function is. That's the cosine so let's go ahead and work it out cosine of the angle 33 degrees is going to equal adjacent over hypotenuse and that would be W / 4.5 go ahead and calculate the cosine of 33 degrees for that I am getting 0.8 and 8 38839 and that equals W / 4.5 go ahead and multiply both sides .839 x 4.5 is going to give me 3.7 76 approximately what w equals let's continue with the samples all write the inverse notation I have here right triangle I have a side length and I have a hypotenuse and I don't have the angle but from the vantage point what relationships do I have the fours the opposite side of the angle and the Seven is the hypotenuse opposite over hypotenuse what is that what is that find good so now we have sine of the angle Theta which is my unknown that equals 4/7 can you figure out what the English so how do I do this while I'm going to go ahead and take the inverse function so the angle is going to equal the inverse what's the sine function in that's how you notated with a little negative 1 exponent of 4/7 to go ahead and calculate sevens in your calculator 4/7 it's going to give me I have data equals the inverse of  4/7 and I got 0 point I'm going to round to the thousands here five seven 571 alright so to calculate your inverse look for on your platers the following symbol is it on right here for you  Wisconsin latest will have this function  that's your inverse sometimes it'll be bring this way find an H right sometimes you are going to have to hit the second button or second function button on your calculators and then that'll be followed by hitting that  sign button on your calculators so it could be a combination so figure out how to get the inverse this number you can go ahead and punch and listen in the sign of that  I am getting  angle of 60 point what is the 252-5425 for degrees alright is it thank you very much I will see you guys soon bye bye

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