Solving Trigonometric Equations | A-level Mathematics

Solving trigonometric equations - from the basics to more challenging problems. This is a large topic but with practice and a good understanding of the fundamentals you can master it quickly.
*At 11:53 the interval should be for x, not theta
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00:00 intro
00:58 Level 1 equations
11:19 Level 2 equations
23:49 Level 3 equations

[@denas4051]

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😁

[@TechyMage]

31:59 Use, cos3A=4cos³A-3cosA

[@mrmovie.102]

Your explanation is straight to the point, I respect it.

[@IODell]

Excellent video. Thank you.

[@reimm9094]

srsly an amazing video everything is in it looooove it

[@mybloodyvacuum]

Great video, thank you

[@tyer4946]

thank you for this

[@samuelnelson7371]

Fantastic video

[@finntozer9319]

thanks maths guy you the man

[@goChina33]

Excellent 👍 very clear

[@muhammadsuleimanhussain-jf9nz]

VERY NICE MASHA ALLAH

[@allmight1670]

thanks so much

[@NihonWoYumemite]

Thanks for showing the trickier problems! Massive help

[@leanne.]

thanks!

[@nethunamaraweera3878]

thanks man

[@pathioussikamanga3285]

Thank you

[@fatimahjanjua6915]

😍😍😍

[@JPL454]

Remember people, when you have two different trignometric relations on a equation just swap one of them with transformations

[@kentanakamura3263]

perfect

[@deplannest6191]

Thnkz you so much but the last eqn needs more explanations

[@user-jf6uq9ig5z]

The last one was too much. However, it is a really helpful video

[@ELLIPTICALWR]

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?

[@maths.explained]

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 :)

[@jovanyabushkara3858]

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

[@ELLIPTICALWR]

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

[@maths.explained]

Yes there are a number of methods to solve it. I don’t always show “the best way”. Thanks for sharing :)

[@user-qg6iy3tt1c]

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

[@maths.explained]

Because sinx has a positive and negative value. If it was only positive you would be correct

[@hegel0076]

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?

[@maths.explained]

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.

[@AA-fb5gq]

thank yoy \

[@novice6236]

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]

[@maths.explained]

I highly recommend watching my video on the unit circle: kzbin.info/www/bejne/aqW0iWRvbbiHrq8 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.

[@marshalltakunda-cm6xy]

Hi. How dd you get (2Cosx- 1)(Cosx-1) on level two

[@maths.explained]

you need to understand how to factorise quadratic equations before trying that problem: kzbin.info/www/bejne/Z5LUZ4FvrN-DbtU

[@N19N90N9]

16:19 shouldn't it be "-2cos^2θ + 3cosθ - 1 = 0"?

[@maths.explained]

its the same thing if you multiply by -1

[@N19N90N9]

@@maths.explained Ok. Thanks.

[@assylbeksabyrzhan7932]

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?

[@maths.explained]

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 :)

[@assylbeksabyrzhan7932]

@@maths.explainedoh, i got it Thank you!

[@toasteemi]

Wdym by A level we did this in Class 9

[@daleflaherty]

How greedy have you been putting all these ads in. I'm not watching this as I refuse to watch 13 ads!

[@maths.explained]

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 KZbin. But please let me know: no ads or just less ads? Thanks, and sorry for the inconvenience.

[@zonaab8252]

The adds are fine most don’t actually show up, only about 3-4

[@joe653]

@@maths.explained do not remove the ads you need them, its fine its solid content

[@edmarx2325]

@@maths.explained It's ok even if you are greedy, just keep that solid supply of interesting hard problems ^^

[@ThugShaker9]

just get an ad blocker

[@Burningarrow7]

I fucking hate math

[@Burningarrow7]

I genuinely hate you for that last question. How tf do you expect your high school students to know how to solve that?