Advanced Functions 7.5 Solving Linear Trigonometric Equations
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- เผยแพร่เมื่อ 6 ก.พ. 2025
- Solving linear trig equations using some identities and rearranging equations like you used to do in grade 9. We will look at using sketches of the functions to determine the number of solutions and also work with both exact values and decimal answers. I will explain how to determine other solutions by using the period of the function in cases where the k value is not 1, and also talk about the importance of checking the domain restriction to the question.
I stayed up last night 10 pm til 5 am this morning.. watched all of chapter 7...
Watch... Pause... Solve ...
It was fun ...
Very very useful... And unlike most of math vid... Not boring.. but fun
Not sure you should be working all night like that but ... good for you!! 😊
ive had to watch this 5 times but I'm slowly starting to understand. thank you for this lovely video
That’s why students revisit the lessons. Sometimes once in a classroom just doesn’t don’t! 😊
Thank you so much for this video! It really helped me prepare for my test tmrw! : )
Good luck tomorrow! Although luck has nothing to do with being prepared!
@@mshavrotscanadianuniversit6234 Thank you Ms. Havrot!
Let me know how it goes!
@@mshavrotscanadianuniversit6234 I think it went great! Thank you so much for your help!
These videos are a lifesaver!
This is recent videos! This helped me a lot. We had supply teacher today and he barely explained the concept and equation with double angle was difficult to understand.
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My question is that the example with sin2x and cos2x, you got 4 answers( i understood the concept of adding period), and arent 5pi/8 and 13pi/8 in Quad 2 and 4 which tangent is negative? Can you explain about this?
Can you tell me the point on the video that you are referring to? That way I’ll be able to explain it without trying to find the spot. 😊(tell me the time on the video please)
Okay, I have had time to find the question that you are asking about. What you haven't grasped is that we have changed the period of the function because it is 2x . Take a look again at the graph ( at 13:06 ). The period for the tangent function without a compression is π but now we have the period is π/2. Hope that helps! Good question!
@@mshavrotscanadianuniversit6234 Thank you, Ms.Havrot!! I think I'm prepared for tomorrow's test:)
Hi ms,
i was wondering where the 5pi over 6 came from at 2:08
You use the pi/6 which is where sinx = 1/2 and subtract it from 6pi/6 to get the second value where sin x = 1/2 between 0 and 2pi. You can check that on your calculator if you want 😊
@@mshavrotscanadianuniversit6234thank you😊
10:52 Isn't the period of the first function: tan 2x = 1 just *pi* ?
Since k = 2, and the formula for the period is: [ period = 2pi/k ],
hence the answer for the period should be: *pi* . ---->> period = 2pi/2 = *pi* .
That is, the *period* of tan (2x) = 1 is: *pi* , not pi/2 as you indicate on the video.
Unless, it takes tan(x) only *pi* to complete one cycle.
Yes, the period for the tangent function is pi, sine and cosine have periods of 2 pi
@@mshavrotscanadianuniversit6234 Thank you very much.
Hi miss! I have a question. At 9:09 I’m confused of where tan went when you were doing the tan2theta = 1
First ask yourself where is tanθ=1 and you then would say when θ = pi/4
But we don’t have tanθ , we have tan2θ. So what I did was solve for θ and then divide by 2. Let me know if you get it. (Maybe watch a second time)
Hello Ms.Havrot, this video was amazing, while doing the homework problems in 7.5, i've been having a problem with question.12 pg.428, do you mind helping me out with that? Thanks so much for these videos btw!!
Did you try sketching it? Or check the solution manual here www.emmell.org/wp-content/uploads/2013/09/MHF4U-Full-Solution-Manual-Small.pdf
Great video! Just wondering, do we need to state restrictions for these?
You should state restrictions I’d there are any, in particular rationals. Please like the videos that you watch (if you like them! 😌)
Tysm Ms Havrot would have been failing math without you 🫂
I’m so happy that I am keeping you passing! Just a little help goes a long way.
Thank you!
Why were you able to make sin2x over cos2x = 1 , I don't see that on the identities sheet provided from my teacher.
If you are referring to 7:43 on the video (please refer to a time when you ask a question so I can find it faster) ... what I did to solve the equation was divide both sides by cos2x to begin with which gave me one on the right hand side. Then I used the identity that 2sinxcosx is sin2x, which then gave me tan2x.
@@mshavrotscanadianuniversit6234 Hi I was referring to 8:35 on the video when you stated sin2x/cos2x = 1 , I was wondering how you determined it was 1, since they don't have the same numerator and denominator, and I don't see it as a trig identity on my identity sheet.
Thanks, Ms. Havrot
Sin 2x / cos2x is NOT an identity. It was only equal to one because I am solving an equation where I divided the right hand side by cos2x and That was what made the 1 on that side.
Ms Havrot's Canadian University Math Prerequisites Oh yea I don’t know why I didn’t see that. I always make dumb mistakes like that on test like writing 3^2 as 6 and not 9 :( . Anyways thanks for your help Ms Havrot!
Remember to just take your time! And always double check your work. There’s always plenty of time for exams.