Solve Trigonometric Inequalities with Help of Graph and Basic Concepts

[lpr]

man, I don't know where you are. but I hope you are as happy as I was when I understood trigonometric inequalities

[arinzeanthony]

Nice video.
But I'm confused at some point.
I don't know if my approach is wrong, but here's how i did it for Q2.
If sec²x<=4, then
1/cos²x<=4 which implies that
1-4cos²x<=0.
When you solve this, you'll notice that there are more solutions to it than you gave within the limits of [0, 2π].
For instance, 0 is a solution.
Because sec²0 is 1, and 1 is less than four.
But i don't see it in your solution.
So....

[jonilamurtezi]

Sin(x)=1/2 => x=pi/3 or x=pi/6? 27:35

[HeartDy_]

Lets take a small break i was like *okay* then a reindeer appears awww

[dogstale]

Why isn't 5pi/4 not included? Isn't it neg. and less than root 2. What am I missing? Can anyone help me to understand why he omitted this value from the range? Thx.

[rashwonsingkai]

Pls make a video on how to solve absolute trig inequalities 🙏🙏

[keithhowen]

I think you must have misread sec^2 x <= 4 as sec^2 x >= 4 (at the second question). Because sec^2 of pi/2 is definitely not smaller than 4, and also for 3pi/2.

[AnilKumar-tqjq]

What is domain and range of square root of sinx

[amberliwentee]

17:11 There might be some mistakes the "angles of 3rd and 4th quadrant" I think I should be 5pi/4 and 7pi/4 I was confused sir👀

[christopherreid]

If we solve for secx is less than square root of 2 using cosx graph we would get the same answer?

[Babyselina-wwru]

I think ther're some mistakes in the final solution 19:07 and also i noticed that in the 3 and 4 quadrants it should be 5pi/4and 7pi/4, however i like your videos❤

[gaddamalekhya]

Thank you so much .sir, it helped me a lot

[sumanratra]

Sir what are solution of sin2x>sin60 degree

[basavarajmunavalli]

Sir your videos are interesting and useful, I am thankful to you for making available on public domain like you tube .
My request is that please post a minimum of 45 mins videos, as the length is enough to at least understand better . A lot of thanks for your services .
Best regards
Basavaraj Munavalli
Bangalore

[ALifein]

There’s an asymptote in secant functions

[amberliwentee]

Well I got more or less the same as Q2 (right before this question) so my answer is shown as below
Q3
[ π/4, 3π/4 ] U [ 5π/4, 7π/4 ]

*I wrote include/equal behind the 3π/4 and 7π/4 is because since it is cos x = ±1/√2, the title stated ≤, then I assumed that it is cos x ≤ ±1/√2, then it be -1/√2 ≤ cos x ≤ +1/√2. What I try to mean is for the -1/√2 and +1/√2 both will include it's respective angle as the "include side" . That is why i put ] instead of).

Just like Q2 shown
The answer is shown
[ π/3, 2/3π] U [ 4π/3, 5π/3]
Because I was thinking is if the concept of -1/2 ≤ cos x ≤ +1/2 which sir indicated this in a form of cos x = ± 1/2 as well as how you show to plot the x intervals.

Both ± 1/2 exist instead of just positive 1/2 is caused by the (less than sign) ≤, which you taught me that it include negative values as well.

As for Q1 it is [ π/3, π/2) U [ 4π/3, 3π/2) I understood why it put )not include behind the π/2 and 3π/2 is because of the nature of tangent graph there broken to pieces by asymptotes that's why they cannot include. (the tangent graph is not continuous along with x-axis)

Sir, plz help me to understand my misery 👀 I am so confused of Q3

I need help sir.

[rumanaruma]

Sir, do you have any Facebook group page for study.?