this is the most clear and concise explanation of this topic i have found. Coming from someone who isnt doing great at this topic, this video is great, thanks😁
9:23 The question was (I'll use 0 as a representative of theta) Solve the equation sin0 + cos0 = 0 You rearranged the formula so you got sin0/cos0 = -1 The completed the rearrangement by turning sin0/cos0 into tan0. So you ended up with tan0 = -1 To get 0 on it's own you formed the formula 0 = tan-1 (-1) I get all of that. What I don't get is why you used the sin equation (180 - x) instead of the tan equation (180 + x) to get the values, seeing as Tan is the only one there, and not sin. Would the values not be: x = [45] and [225]
I highly recommend watching my video on the unit circle: ruclips.net/video/4tQX198STxM/видео.html it seems like you are getting confused at the last step of finding values of theta, which involves interpreting the final trig equation (eg tanx=-1) and understanding in which quadrant those angles will be.
You could try it. Generally the t formula is used when it will be more efficient than other methods. I don’t think it would be helpful in these examples as it is possible to see a clear method available but you could try and see if it gives faster solutions. Also, this video was made for A-level maths where we don’t use the t formula yet, so if you want harder problems I recommend looking at some further maths problems :)
yes ofc just write t=sinx or t=cosx ,and rewrite the equation with t like: sinx^2+sinx-2 "(t=sinx)" rewrite it as: t^2+t-2 then lets say the t is equal to -1,1/2: write sinx=-1 and sinx=1/2 then solve the trigonometry for both sinx but remember sinx and cosx must ="-1
I have a question, answer would be very helpful. Why do we not have 6 answers in last exercise, isn't it that cosine has the same value for two different angles? Cos(20°) is the same as cos(340°) so why isn't 340° also one of the answers?
Why in the 2nd problem of level 2 equations didn't you simplify the term (1-cosA ) Because we can rewrite 2(1- (cosA)^2) as difference of squares and on right-hand-side we can get the same with 3(1-cosA) and then we will get only 1 solution. But how it is possible?
This works fine. I suppose you are dividing both sides by 1-cosA? This is only possible if cosA =/= 1. Then you need to check if cosA=1 is a solution, which it is. So you will get the same answer :)
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this is the most clear and concise explanation of this topic i have found. Coming from someone who isnt doing great at this topic, this video is great, thanks😁
31:59 Use, cos3A=4cos³A-3cosA
Excellent video. Thank you.
srsly an amazing video everything is in it looooove it
Excellent 👍 very clear
Remember people, when you have two different trignometric relations on a equation just swap one of them with transformations
THANK YOU SIR
Thanks for showing the trickier problems! Massive help
Fantastic video
9:23 The question was
(I'll use 0 as a representative of theta)
Solve the equation sin0 + cos0 = 0
You rearranged the formula so you got sin0/cos0 = -1
The completed the rearrangement by turning sin0/cos0 into tan0. So you ended up with
tan0 = -1
To get 0 on it's own you formed the formula 0 = tan-1 (-1)
I get all of that. What I don't get is why you used the sin equation (180 - x) instead of the tan equation (180 + x) to get the values, seeing as Tan is the only one there, and not sin.
Would the values not be:
x = [45] and [225]
I highly recommend watching my video on the unit circle: ruclips.net/video/4tQX198STxM/видео.html it seems like you are getting confused at the last step of finding values of theta, which involves interpreting the final trig equation (eg tanx=-1) and understanding in which quadrant those angles will be.
Thnkz you so much but the last eqn needs more explanations
thank you for this
the last one can be done by identifying it is a hidden cubic and can be solved using a polynomial solver or factor therom that way
Yes there are a number of methods to solve it. I don’t always show “the best way”. Thanks for sharing :)
thanks maths guy you the man
does the t formulae work for when there is like a sin squared or cos squared in the equation., or like translation of sin/cos?
You could try it. Generally the t formula is used when it will be more efficient than other methods. I don’t think it would be helpful in these examples as it is possible to see a clear method available but you could try and see if it gives faster solutions. Also, this video was made for A-level maths where we don’t use the t formula yet, so if you want harder problems I recommend looking at some further maths problems :)
yes ofc just write t=sinx or t=cosx ,and rewrite the equation with t
like: sinx^2+sinx-2 "(t=sinx)" rewrite it as: t^2+t-2 then lets say the t is equal to -1,1/2: write sinx=-1 and sinx=1/2 then solve the trigonometry for both sinx
but remember sinx and cosx must ="-1
16:19 shouldn't it be "-2cos^2θ + 3cosθ - 1 = 0"?
its the same thing if you multiply by -1
@@mathonify Ok. Thanks.
I have a question, answer would be very helpful. Why do we not have 6 answers in last exercise, isn't it that cosine has the same value for two different angles? Cos(20°) is the same as cos(340°) so why isn't 340° also one of the answers?
The question gives an interval for theta between 0 and 180 degrees. If the interval was 0 to 360 then 340 degrees would be a valid solution.
VERY NICE MASHA ALLAH
thanks man
Why in the 2nd problem of level 2 equations didn't you simplify the term (1-cosA ) Because we can rewrite 2(1- (cosA)^2) as difference of squares and on right-hand-side we can get the same with 3(1-cosA) and then we will get only 1 solution. But how it is possible?
This works fine. I suppose you are dividing both sides by 1-cosA? This is only possible if cosA =/= 1. Then you need to check if cosA=1 is a solution, which it is. So you will get the same answer :)
@@mathonifyoh, i got it Thank you!
thanks!
The last one was too much. However, it is a really helpful video
Thank you
Hi. How dd you get (2Cosx- 1)(Cosx-1) on level two
you need to understand how to factorise quadratic equations before trying that problem: ruclips.net/video/1aq6N9wzP8s/видео.html
I'm confused on the 4th question why were there 4 values I thought that with sin up to 360 would only have 2 values 57.69, 122.3
Because sinx has a positive and negative value. If it was only positive you would be correct
thanks so much
perfect
thank yoy \
😍😍😍
Wdym by A level we did this in Class 9
How greedy have you been putting all these ads in. I'm not watching this as I refuse to watch 13 ads!
I do not manually place the ad breaks, I just turn them on. I don’t know why there are so many ads. If you suggest I should turn off all ads then I will consider it. I’m just not sure how I could continue with RUclips. But please let me know: no ads or just less ads? Thanks, and sorry for the inconvenience.
The adds are fine most don’t actually show up, only about 3-4
@@mathonify do not remove the ads you need them, its fine its solid content
@@mathonify
It's ok even if you are greedy, just keep that solid supply of interesting hard problems ^^
just get an ad blocker
I fucking hate math
I genuinely hate you for that last question. How tf do you expect your high school students to know how to solve that?