Solving Trigonometric Equations

We solved so many equations when studying algebra. Now that we understand trig functions, as well as inverse trig functions, we are ready to solve trigonometric equations. This will combine an understanding of trigonometry with some of the techniques we learned in algebra, and in the end, all we are doing is finding the value of x that makes the equation true, so it's nothing new!
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[@sarav.g8569]

I can't explain how much this has helped; I have a test tomorrow that could save my grade for the class. I have nothing against my teacher; she is very nice, but sometimes she does the steps in her head, and I get lost. This has helped me so much.😭

[@andrewneems]

Well i am struggleing with all of trigonometric identities and i feel like i am stupid even though i am not but this is hard or it appears to be erksom

[@MIZORAM_mafaka_hnamte]

_Love this channel... so much_

[@ikramullah8892]

great explanation..... good channel

[@ubermenschexplorer4910]

For anyone confused at last number 2, there are actually 6 solutions within 0-2pi, for x 1. Pi/12 2. 5pi/12 3. 9pi/12 4. 13pi/12 5. 17pi/12 6. 21pi/12 Hope this helps :).

[@ckarcher4504]

me toooo!

[@americanmathematics5478]

I love trigonometric equations and trigonometric graphs

[@hecunotmakingalogisquad5785]

check with a doctor you are not okay

[@justsomeguywithamask1564]

-said no one ever

[@boston.0703]

⁠@@hecunotmakingalogisquad5785 -said a gamer who doesn’t accomplish anything and just stays home all day and plays games for no reason

[@boston.0703]

@@justsomeguywithamask1564 - said a gamer who doesn’t accomplish anything and just stays home all day and plays games for no reason

[@CurryNotFound]

5:11 How did you factor that equation?

[@AhamedKabeer-wn1jb]

Thnkz

[@carlatoting5692]

Hello dear professor dave. I am looking how to solve trigonometric equations and Im glad that I understand now because you explained it well. But I want some favor , Sir May i use some of your explanation to my report ?

[@RadoHudran]

I think he'll be happy if you share his video, as long as you don't use the entire video

[@samana4499]

Tank you ❤️❤️❤️

[@jackf260]

4:40 why are some 2(pi)n and some just (pi)n?

[@ivorscott]

Also wondering why..

[@tmchannel8483]

for tangent, the possible solutions were in quadrant 1 and 3, which are directly opposite each other. therefore you only need to go around halfway (pi) to go from one valid solution to the other.

[@terukun5645]

How do we solve the angle of elevation for the first problem without using a calculator?

[@ProfessorDaveExplains]

Eh, pretty tough, you would need a bunch of trig identities. I cover them later in the series. But no one would expect you to use them, calculators are fair game in trig.

[@terukun5645]

@@ProfessorDaveExplains Oh okay, thank you!

[@lameyeast7085]

​@@ProfessorDaveExplains prof. I have a question In the last equation you showed us (1-cos²x) + 2cos²x =0 1+cos²x =0 Cos²x = -1 cos x = sqrt(-1) Wouldn't cos x be imaginary Pls explain

[@arrogant_little_punk9701]

Can anyone explain 1:44 what to multiply by what cause I'm getting 180 instead of 144

[@wramenx5903]

Not sure if you still need it but here's an explanation. 100×tan55.3 =144

[@arrogant_little_punk9701]

@@wramenx5903 thnx bro

[@Nemoguzapomnit]

3cos(3x+1)=3, the answer is (2πk-1)/3. And thx for your video!

[@ProfessorDaveExplains]

it says over the interval of zero to two pi, so there is only one answer

[@Nemoguzapomnit]

oh yeas sry, my bad. Missed that

[@Nemoguzapomnit]

w8 if 0 to 2π then how answer can be negative? form 0 to 2π (2π-1)/3 you can check it in graphic calculator.

[@ProfessorDaveExplains]

the limitations just mean that when taking the inverse cosine of one, you get zero, and not 8pi, or 800pi, etc, any of the other infinite number of valid answers for that inverse cosine. it does not mean a limitation on what x can be.

[@Digitalbandits99]

07:21 after solving this, is the answer imaginary?

[@LoveIssa-mj9em]

Yess

[@harshsinghal4342]

thanks but i have a problem with this concept. in the first exercise problem x= -1/3 is not in the interval 0 to 2*pi, it is negative. so what do we mean when we say that we are solving this in the interval 0 to 2*pi?

[@ProfessorDaveExplains]

so we are just saying that in order to properly take the inverse cosine. the inverse cosine of one is zero, or two pi, or four pi, etc, but we just consider it to be equal to be zero to keep things simple, and then continue solving from there.

[@muammaralmansour8070]

bro stop skipping the small steps i cant understand this

[@ok22283]

thats ur math basics' problem

[@themathematicstutor4092]

Sounds like a you problem.

[@HassanStudies]

skill issue

[@tGoldenPhoenix]

Done.

[@davidsweeney111]

My teacher likes me to use the word 'subtended' when doing trig, but I dont know what it means.

[@lolygagger5991]

you're really saving my ass here professor dave, thx.