 All right, let's go over the quiz here and sir key always getting everything right so on your test I'll probably have you convert something to degrees 5 pi by 12 I'll probably keep it a little simpler than that, but let's do 5 pi by 12 5 Pi by 12 and the conversion factor is since I want degrees I want degrees on the top the pi on the bottom The pies cancel and I know that 6 goes into 180 and 12 pretty easily I know that 180 divided by 6 is 30 I know that 12 divided by 6 is 2 and then I would say hey 2 goes into 30 and 2 1 and 15 in fact this whole thing works out to 5 times 15 which I'm pretty sure is 75 degrees Number one convert or sorry number two convert 220 to radians, so it's going to be 220 times Pi over 180 it says leave your answer as an exact value in terms of pi I Would expect that it's fair game to ask you to clue in that the zeros will cancel it divide by 10 divide by 10 I would even expect mitzv that it's fair game to say divide by 2 divide by 2 So you would say this is an 11 and this is a 9 and hopefully you would get 11 pi by 9 One more Find two co-terminal angles for 11 pi by 4. Okay. I'm gonna add to pi wait a minute. That's dumb. Mr. Do it Spencer. What's my denominator here? You know what? I'm gonna add 8 pi by 4 and I'm also going to subtract 8 pi by 4 It looks like 19 pi by 4 It looks like 11 take away 8 3 pi by 4 Did anybody add another time if you add 8 pi 27 pi by 4 would work or are there any other answers out there? Nobody's had to phase shift out to the million just to annoy me We'll call that yeah, we'll leave a couple years ago did that it was funny once but now just State the principal angle well the principal angle I'll call that P of theta. I just made that up right now. I guess 3 pi by 4 That's the angle between 0 and 2 pi. That's the I sort of called it Eric the lowest terms angle number 4 curveball a little They told me a number 4 that x equals 2 That y equals negative 4. I should be able to find out what r is well R is going to be the square root of x squared plus y squared It's going to be the square root of 16 plus 4. I think r ends up being root 20 or 2 root 5 Mr. Duk would you make us to the if I gave you this it would be a multiple choice nasty question And I would probably have that in the answer so I'd expect that you clue in that when you get a root 20 You can pull out your math can and rewrite square roots in mixed form Now what well They want me to go sine theta minus secant theta sine is y over r negative 4 all over 2 root 5 minus Secant secant secant goes with cosine cosine is x over r secant is r over x to root 5 Over 2 By the way, if I'm marking this if you found r properly that gets you a half mark, but we'll keep going in there And if you wrote this that would get you a half mark How do I multiply fractions multiplying fractions Justin? That's the easy one top times top bottom times bottom How do I divide fractions almost as easy flip the second one and multiply? Adding and subtracting fractions. That's the pain common Denominator although I think what I would do I would choose to reduce these fractions first I would choose to say you know what I Got a four on top. I got a two right here. This is really negative two over root 5 minus I Got a two on top and a two on the bottom the twos would cancel root 5 Over one now if you didn't do that don't freak out. You can also reduce later. I need a common denominator Sabina what's underneath this fraction? What's underneath here? You know my common denominator is It's gonna be root 5 I'm gonna rewrite this whole thing as one big fraction Over root 5 what would I multiply a root 5 by to change it into a root 5? It's a trick question So the negative 2 just drops down like a domino and the minus sign drops down What would I multiply a 1 by to change it into a root 5 why I've multiplied by root 5 and by root 5 Multiplying also by a 1 but by a funny-looking one And on the top I would have root 5 root 5 or root 5 squared or just plain old holy smokes by In fact, I think this whole thing works out to negative 7 over root 5 Now if you've got that that gets you 3 out of 3 if you didn't see the reducing thing I think you'd have this negative 14 all over 2 root 5 I Guess I take that but let's reduce numbers by numbers roots by roots any other weird answers out there You're wondering about yes Oh, you rationalize it all clever use so you said negative 7 root 5 all over 5 I'll take that too, and I'll even smile in your direction and say oh By the way, I would also then go half mark for that half mark for that half mark for that And then one mark for the answer something like that Any other weird answers out there Should do it cuz maybe a bunch of those nine I'd consider this a curveball so there's gonna be on your multiple choice probably two or three But not 15 And then we're back into familiar territory amplitude for one mark period Two pi over three pi, which I'm pretty sure is just plain old two over three one mark Phase shift Emily is there an alarm bell? Nope, so phase shift is just five or five right a little better Vertical displacement Seven one mark each number six Describe the details of and graph this Emily is there an alarm bell? Yeah Yeah, I Need to rewrite this as Y equals negative three Coasts I need to factor out the one half minus one Well, there's gonna be a theta There's gonna be a plus What's gonna be left in the brackets when I factor out a one half? Well, mr. Dewick said that factoring is equivalent to dividing it really what's going to be there is pi over four divided by one half How do I divide by a fraction dummy So you're telling me it's really gonna be pi over four times two over one Which would give you two pi over four or low and behold just pi over two yes, it is Your amplitude is three your period is Two pi over a half. Hey, it's four pi Your phase shift is negative pi by two or pi by two left Your vertical displacement is negative one Ah, but we're not done mr. Dewick always said it was worth finding two more things It was worth taking the period and dividing it by four Which gives me a lovely pie my dots are going to be pie apart And then it was worth finding a good scale so that instead of saying my dots are pie apart I could say my dots are how many squares apart That's over one. That's over two. That's over one. You know what I think my horizontal scale Is gonna be pi by two and I'll call this two pi by two and I'll call this Eight pi by two the period is gonna be eight squares And every dot is gonna be every two squares Let's bring in my oh, what did I say I did first vertical displacement? I did first negative one amplitude three one two three Amplitude three one two three negative four Each square is going to be pi by two so I'll call this two pi by two four pi by two Six pi by two Eight pi by two. I'm really going up by pies, but I don't want to reduce why make myself do extra thinking Negative two pi by two negative four pi by two good night phase shift Okay, my first point is gonna be one square left somewhere on that line Brett what am I graphing positive sign negative sign positive coast or negative coast? A negative coast starts where you like and then every two squares one two middle One two top one two middle one two bottom one two middle I've run out of room. Hey, let's go backwards middle top Middle bottom Yes, the fun helps Now if you used a different scale mitzvah what you're really looking for is this Do you have a point that goes through? negative pi by two negative four and does your next point go through three pi by two positive two Because you could have gone with a scale of for some reason pi by fours would also work it would just mean that Every four squares would be a dot and your period will be 16 squares long and the phase shift would be two squares left, but the Coordnance would match my destiny How do I mark this so one mark one mark one mark one mark for each of those two marks for the graph What I would probably do is give you a half mark if you had the amplitude and vertical displacement, right? So half mark for the Amplitudes half marks for the vertical displacement and then one mark for getting the points right so half mark off for each point That's wrong. So give two points wrong. Sorry. The best you do is one or two Is that okay? number seven oh They double a so normally we said the range was vertical displacement and then a down and a up from there If they double it, it's gonna be vertical displacement and then two way down and two way up from there That bad boy. What's the domain of y equals tan two theta? I'm gonna ignore it for the two for a second. I know that normally tangent doesn't exist at plus or minus 90 Plus or minus pi by two. Oh normally X can't be pi over two and Pi apart normally But Brett how has this been changed? We've replaced theta with what? We've replaced theta With two theta. That's a horizontal Compression by a half. You know what? In our case now, it's gonna be pi over four plus multiples of pi over two Where n is an integer? Half mark half mark you forgot that take off a half mark. What's the domain and range of y equals four cosy kent? Hmm. Well normally normally the range was Everything bigger than or touching one Everything smaller than or touching negative one but Spencer what's right there? Vertical or horizontal? Really you think that's right next to the theta tucked inside the function. I think it's vertical Vertical what I think that's a vertical Expansion by four I Think we'll check out our graphing calculator in a second, but I'm pretty sure Domain Cosy kent goes with what cosy kent goes with what sign? so where sign theta equals zero that's where X won't exist for cosy kent where to sign theta equals zero here here here. Oh x can't be zero plus multiples of pi where n is an integer Now sandally normally we would erase the zero plus for a secant There is an actual number there and so we leave the number there I think secant starts out at pi by Two plus multiples of pi. I can't even remember. I just derive it every time One mark one mark. Let me double check. Does this work? I'm a little worried about that for cosy kent. Let's see calculator up clear How would I graph cosy kent? Oh? four divided by sine x And I'm gonna cheat. I'm gonna go zoom trig What? Window off. I'm going from negative four to positive four I probably need to go a little more than that. How about negative eight to positive eight? Hey, that looks good. Sure. I'm in Looks good So one mark one mark Give yourself a score, please out of 21 But I don't want to collect these because I won't be seeing you between now and the quiz test time will I? No So you know what? I'm just plain not gonna count this one If you did good good if you didn't then I guess that's good, but well, you'll figure it out Okay, okay, listen up for a second here I Noticed that something strange happened when I printed trig review number one for you This is what we gave you when I was away last week for some reason only every other page printed And as I was going through it I went well a lot of the weird curveball we practice questions stuff with cosy can't see can't Those seemed to be the ones that were on the pages that didn't print. So what I just gave you is actually trig review number one the second half the part that didn't show up and I'd like to recommend a few more questions wink wink nudge nudge. I like these questions. I like these questions I like these questions Okay So from the section that I just gave you six oh heck Six through nine and you'll notice seven and eight or asymptote and domain questions about ugly cousin and reciprocals 15 16 17 why don't you just say 15 through okay fine? You know what mr. Duke? 15 through 17 comma 22 through 24 31 32 34 41 42 x 41 42 43 41 through 44 51 54 59 60 62 63 70 72 77 78 79 80 85 There's a lot of them. I noticed that the section you had seemed to be missing a lot of the questions that I thought were great practice 94 96 105 112 121 122 131 132 133 And the written section that you can temporarily ignore Most of that is on trig part two. What's gonna be your written section? I already told you, but I'll say it again two graphs and Then probably four trig equations one of which will be a reciprocal one of which will be a quadratic One of which will be a weird and plus or my like alarm bell equals negative one zero or one There'll be one of the axes up to the inner circle and one of which will have a domain change I Was gonna do a lesson, but I think what I'm gonna do is just simply say hey work on this I gave you two reviews I would say Target this one right now. So what do we have grand total one two three four five six seven eight nine ten eleven twelve 13 14 15 16 17 18 19 20 20 5 to 6 to 7 to 8 29 30 31 32 Well lots of questions like 60 or so Started continuing to count Again Trevor use your judgment if you get like for example a whole bunch of these are Cast rule questions if you can glance at it and do it in your head Check if you're right skip that or A lot of them are exact value questions if you're doing exact values in your sleep you only do the tough ones Oh, see can't that's trickier than sign say or something like that Okay, yeah, yeah Is this do before the test? Well Sure, I guess I'll say how about of the two reviews that I gave you I would love this one here handed in the day of the test I'll give it back to you though because half the questions apply to the next part of the trig unit to So I'll get it back to you as soon as I can Any questions at all? So I normally don't press pause like this, but I thought about it over the weekend And I was boy, it's missing a lot of good questions In fact, I think there's more questions here than what I originally assigned. I'm shutting up