I think the best thing to do is take your time with it. When I first started doing this, I usually rushed it and messed up a lot. Than one day, I'm like, lets slow this down it dramatically helped. I could basically do all of them 😀😀😀 I feel like if you take your time (and write a little bit slower) you could understand everything better and plan your moves as you write down the equation...Very simple yet very effective. Hope this helps, have a wonderful day, or night XD
Excellent advice! I always liked identities because to me they were like a puzzle that you know the answer to. Like unscrambling a word! Thanks for your comment. 😊
Don’t panic! The identities are challenging but there are always part marks for them if you can’t get to the final step. The rest of the chapter is not as difficult. Logarithms you will find easy. Hang in there! The end is within sight. Congrats on your 90!!! Well done 👍🏻
My teacher says we are only allowed to work with the left side of an equal to make it equal to the right side so I am a little confused but your method makes a lot more sense to me
It's a bit hard for a grade 12 class but I'm sure you will understand why we normally work to simplify to sine and cosines where possible. It is still quite legitimate to work both sides of the equation. mshavrot.pbworks.com/w/file/fetch/142667970/Trig%20identity%20.pdf
because it was minus a minus = plus Rewind to when I put 1 - 2 sin^2 x in brackets and the emphasis I put on making sure you multiply everything in that bracket by -1
Ma'am may I ask if a trigonometric equation with a sigma on the right-hand side while theta on the left-hand side will be True or False when verified? Example: Sin (sigma) = Sin (theta)
That depends on the values for sigma and theta. As you know sin30 = sin150 and sin210=sin330 so it could be true but you would need to know their values.
@@mshavrotscanadianuniversit6234 Ma'am how about this equation, where I need to prove the identity: Tan^ (sigma/2) = (csc theta - cot theta)^2 I got the answer: Tan^2 (sigma/2) = Tan^2 (theta/2) Ma'am is this True or False? There's no given value
I would say that MAYBE it was a typo and that it was meant to all be sigma or theta OR that in the end you would give an explanation as to the values of theta and sigma that would make it true.
I understand! Do each one a few times and you will start to see that there are patterns to look for and remember that as long as you get something down on paper, even one substitution, it is better than leaving it blank.
That's up to your teacher. That doesn't mean that you can't work with the other side on a separate piece of paper and then work backwards with the other side when you reach the same point.
Just remember that proving trig identities is only one part of this chapter. Make sure you know how to do everything else. When doing the identities follow the suggestions I outlined and even if you only get part of it you will be sure to get some marks. Try the practice test, go over all the identities that you have solutions to. Look for common denominators, possible quadratic equations places where you can substitute in for double angles or other Pythagorean identities. If you are close just write the concluding statement that ls= rs Always do what you know first. Don’t waste time struggling with a question that is stumping you. Come back to it after you do what you know well. Remember that logarithms (if you haven’t covered them yet) are easy! Let me know how it goes, and good luck!
Hello there! Can you please help me prove this identity? Please, please 🥺 I have been solving this for 3 days now and I still can't figure it out. 1+sin (x)+cos (x)/1+sin (x)-cos (x)=1+cos (x)/sin (x)
okay ... what you need to do is, working with the lhs multiply both numerator and denominator by 1 + cosx LEAVE the numerator alone because the goal here is to somehow get rid of what was originally in the numerator. Now, expand the denominator. When you do that you will get an identity 1 - [cosx]^2 = [sinx]^2 and two other terms will cancel out. Then factor out a sinx and magic happens! Try this first, then check the answer that I will post right below this explanation. Good question!!
Don't peak! Try it first. Happy New Year! mshavrot.pbworks.com/f/trig%20identity%20%5B1%2Bsin%20(x)%2Bcos%20(x)%5D%20%3A%20%5B1%2Bsin%20(x)-cos%20(x)%5D%20%3D%20%5B1%2Bcos%20(x)%5D%20%3A%20sin%20(x)%20%20%20%20%20.pdf
Definitely the most challenging section. Keep trying, follow the rules, reducing to the sine and cosines when you can, common denominators, keep your identities handy to see if there is something you can replace. Don’t give up!
@@mateofeitor7621 If you are doing your best, it's a great mark. If you haven't performed to your best level then it isn't. I have had students that worked HARD all the time and got 70's. Hard work is what moves you forward; learning good study habits, how to manage your time effectively and persevere at tough tasks is what will get you farther in life than getting a 90. I've seen students that got 90's in grade 12 that have done poorly in university because they didn't learn these skills and just did well without the hard work that you will find is necessary at post secondary institutions. (all that being said ... PUSH hard to the finish line and get yourself a well-deserved 80!)
Thanks, in fact i talked to my teacher the other day and he said that I have great study habits and work ethic. I’m one of the kids in class who always has homework done and practices ALOT.
@@mateofeitor7621 Then you will be successful in life AND if your teacher recognizes your effort I am sure that he will give you the 80 on your final report!
You're the GOAT Ms Havrot
That's an awesome compliment! Thanks : )
your carrying me through math rn thanks for these great vids
Great! Glad to be your “mule” 😂
I think the best thing to do is take your time with it. When I first started doing this, I usually rushed it and messed up a lot. Than one day, I'm like, lets slow this down it dramatically helped. I could basically do all of them 😀😀😀 I feel like if you take your time (and write a little bit slower) you could understand everything better and plan your moves as you write down the equation...Very simple yet very effective. Hope this helps, have a wonderful day, or night XD
Excellent advice! I always liked identities because to me they were like a puzzle that you know the answer to. Like unscrambling a word! Thanks for your comment. 😊
This video is great! Thank you for your help!
Have you subscribed to the channel?
i’m at a 90 rn in advanced functions but i can’t let this test drop my mark. i have this test then logs after
Don’t panic! The identities are challenging but there are always part marks for them if you can’t get to the final step. The rest of the chapter is not as difficult. Logarithms you will find easy. Hang in there! The end is within sight. Congrats on your 90!!! Well done 👍🏻
Thank you so much for your tips for trig identities:)
Have you subscribed to the channel?
Ms Havrot's Canadian University Math Prerequisites yes
My teacher says we are only allowed to work with the left side of an equal to make it equal to the right side so I am a little confused but your method makes a lot more sense to me
Well, your teacher is being a pain! 😂
You can still get a scrap piece of paper and work both sides and then apply what you did to the rhs to the lhs.
@ can u please help me on this question
cosx - cos2x + 2/ 3sinx-sin^2x =1+cosx/sinx
@MisbahFatima-u1n Is it (cosx-cos2x + 2)/[3sinx-sin^(2x)]?
Nice work)
Hi, How could i prove the last example using one side only (the side with 2csc2x)
It's a bit hard for a grade 12 class but I'm sure you will understand why we normally work to simplify to sine and cosines where possible. It is still quite legitimate to work both sides of the equation.
mshavrot.pbworks.com/w/file/fetch/142667970/Trig%20identity%20.pdf
@@mshavrotscanadianuniversit6234 Thank you!!
You are most welcome. 😊
why did the - change to plus before the 2sinx at 14:55
because it was minus a minus = plus Rewind to when I put 1 - 2 sin^2 x in brackets and the emphasis I put on making sure you multiply everything in that bracket by -1
Hello Ms. Havrot. Can you go over cos(x+y)cosy+sin(x+y)siny=cosx. I'm having some trouble with that identity.
Here you go. Looks much harder than it is!
mshavrot.pbworks.com/f/Trig%20identity.pdf
@@mshavrotscanadianuniversit6234 Oh thanks. This really helped. Merry Christmas btw and a happy new year. Hopefully, 2021 is better than 2020.
Well thank you and the same to you!🎄
I’m certain that 2021 will bring true meaning to the saying that hindsight is 2020!
Ma'am may I ask if a trigonometric equation with a sigma on the right-hand side while theta on the left-hand side will be True or False when verified?
Example:
Sin (sigma) = Sin (theta)
That depends on the values for sigma and theta. As you know sin30 = sin150 and sin210=sin330 so it could be true but you would need to know their values.
@@mshavrotscanadianuniversit6234 Ma'am how about this equation, where I need to prove the identity:
Tan^ (sigma/2) = (csc theta - cot theta)^2
I got the answer:
Tan^2 (sigma/2) = Tan^2 (theta/2)
Ma'am is this True or False? There's no given value
I would say that MAYBE it was a typo and that it was meant to all be sigma or theta OR that in the end you would give an explanation as to the values of theta and sigma that would make it true.
@@mshavrotscanadianuniversit6234 Thank you ma'am for your help🥰
Life saver thank you so much
Happy to help!
great video!!!
This is the hardest part of chapter 7 for me miss, hopefully will get it
I understand! Do each one a few times and you will start to see that there are patterns to look for and remember that as long as you get something down on paper, even one substitution, it is better than leaving it blank.
Hey thanks for all the help!! But I really love your pen, what pen do you use?
Ah yes, it is beautiful isn’t it? My daughter bought it for me from a gift shop in Japan when she went there about 5 years ago.
Wait my teacher said we can't work both sides, is that right?
That's up to your teacher. That doesn't mean that you can't work with the other side on a separate piece of paper and then work backwards with the other side when you reach the same point.
I’m very worried about this test any advice?
Just remember that proving trig identities is only one part of this chapter. Make sure you know how to do everything else. When doing the identities follow the suggestions I outlined and even if you only get part of it you will be sure to get some marks. Try the practice test, go over all the identities that you have solutions to. Look for common denominators, possible quadratic equations places where you can substitute in for double angles or other Pythagorean identities. If you are close just write the concluding statement that ls= rs Always do what you know first. Don’t waste time struggling with a question that is stumping you. Come back to it after you do what you know well. Remember that logarithms (if you haven’t covered them yet) are easy! Let me know how it goes, and good luck!
@@mshavrotscanadianuniversit6234 okay thank you
Hello there! Can you please help me prove this identity? Please, please 🥺 I have been solving this for 3 days now and I still can't figure it out.
1+sin (x)+cos (x)/1+sin (x)-cos (x)=1+cos (x)/sin (x)
Hi Anne. Could you please confirm with [ ] what is all in the numerator and denominator?
@@mshavrotscanadianuniversit6234
[1+sin (x)+cos (x)] / [1+sin (x)-cos (x)] = [1+cos (x)] / sin (x)
okay ... what you need to do is, working with the lhs multiply both numerator and denominator by 1 + cosx
LEAVE the numerator alone because the goal here is to somehow get rid of what was originally in the numerator.
Now, expand the denominator. When you do that you will get an identity 1 - [cosx]^2 = [sinx]^2 and two other terms will cancel out. Then factor out a sinx and magic happens! Try this first, then check the answer that I will post right below this explanation. Good question!!
Don't peak! Try it first. Happy New Year!
mshavrot.pbworks.com/f/trig%20identity%20%5B1%2Bsin%20(x)%2Bcos%20(x)%5D%20%3A%20%5B1%2Bsin%20(x)-cos%20(x)%5D%20%3D%20%5B1%2Bcos%20(x)%5D%20%3A%20sin%20(x)%20%20%20%20%20.pdf
@@mshavrotscanadianuniversit6234 Thank you ma'am and Happy New Year 🎇
this is way simpler but my teacher dosent let us work on both sides
You can always work the less difficult side to help you see where you should be heading. (Your teacher is mean! 😆)
I’m having trouble
Definitely the most challenging section. Keep trying, follow the rules, reducing to the sine and cosines when you can, common denominators, keep your identities handy to see if there is something you can replace. Don’t give up!
I have a 79% in my class. Is that okay?
@@mateofeitor7621 If you are doing your best, it's a great mark. If you haven't performed to your best level then it isn't. I have had students that worked HARD all the time and got 70's. Hard work is what moves you forward; learning good study habits, how to manage your time effectively and persevere at tough tasks is what will get you farther in life than getting a 90. I've seen students that got 90's in grade 12 that have done poorly in university because they didn't learn these skills and just did well without the hard work that you will find is necessary at post secondary institutions. (all that being said ... PUSH hard to the finish line and get yourself a well-deserved 80!)
Thanks, in fact i talked to my teacher the other day and he said that I have great study habits and work ethic. I’m one of the kids in class who always has homework done and practices ALOT.
@@mateofeitor7621 Then you will be successful in life AND if your teacher recognizes your effort I am sure that he will give you the 80 on your final report!
Do you want to write my test for me 😀 I don’t get this at all
Practice the ones that I show you over and over until you start to see a pattern. 😊