hello welcome back to the physics 1 course this title of this lesson is called a review of essential trigonometry so every single physics problem that you're gonna work is going to seem challenging to you in the sense that no longer will the problem tell you exactly what you need to do to find the answer so a lot of times almost all of the time when we get past the basic problems there will be an angle of some kind in the problem maybe it's a plane like a wedge where a block is sliding down and the the the plane has an angle to it maybe a baseball is thrown at an angle maybe you're pushing with a force at 35 degrees so or whatever I can go on and on and on there's almost always gonna be an angle in every problem but you're never going to be told hey you need to do the sine or the cosine of the tangent of this angle you're never gonna be told that you're going to need to draw a picture and figure out from your previous knowledge of trig in order what to do you're gonna have to do that yourself and that's why these problems seem difficult so in this lesson we're going to review basic essential trigonometry it's important for you to know that I expect that you have seen this stuff before if you haven't then you need to stop and go to my trig class my trigonometry course and review the basic idea of angles and stuff and I am gonna review as we go through as we solve the problems I'm gonna baby step you as much as I can to review you but still you you need to have been exposed to this material so the first thing we're gonna do the most important things these are these it this is not a review of everything in trigonometry this is the review of the most important things to solve physics problems all right so everything in this lesson is critical fortunately none of it is really hard so if you have a triangle remember this guy he talked about triangles all the time in trigonometry that's what it's all about so you have some kind of triangle and this is a right angle which means it's ninety degrees over in the corner and there's some angle like I told you you might have a wedge a lot of times in physics problems we have a wedge and we call this angle theta so theta don't let it scare you it's just another variable like X or Y this could be 15 degree angle or this could be a 35 degree angle or a 70 degree angle or whatever of course is the angle increases the steepness of this wedge you know gets taller or whatever but this is a general diagram here now we label the different to this triangle we say that relative to this angle the opposite side of this guy we're gonna label it opposite OPP for opposite and relative to this angle this side right here is adjacent adj we call that adjacent so adjacent means the side kind of close to the angle opposite means the side opposite the angle and then the very longest side of every right triangle is called the hypotenuse and I know that you all know that from basic from basic math now also in basic math you learn something called the Pythagorean theorem don't forget Pythagorean theorem don't forget that with right triangles like this you always have the Pythagorean theorem at your disposal the physics problem will never say use the Pythagorean theorem to solve it it'll never tell you that you just have to know that you can use this for every right triangle Pythagorean theorem if the way you learn in geometry is C squared is equal to a squared plus B squared in this equation C is always the hypotenuse it's always the longest side of this triangle the other two since they're added together it really doesn't matter the jacent or opposite doesn't matter what you label them so the way you read this in terms of this triangle that we have right here since C is the hypotenuse will write it as hypotenuse squared is equal to and again I told you it really didn't matter so we'll just call it adjacent squared plus opposite what does this equation mean that means for any right triangle no matter what the angle here is whether it's 15 degrees 30 degrees seven degrees really slender triangle whatever it doesn't matter if you know the length of the hypotenuse and you square it and you know the length of this and this and you square them separately and then you add these to get