Sine or Cosine Writing Equations Given Graph

Is the graph a sine or cosine graph and which function should you use when writing the equation. We discuss sine and cosine equations in this free math video tutorial by Mario's Math Tutoring.
0:11 Example 1 Write the Equation of the Sinusoidal Graph
0:42 Draw Midline of Graph to Find Vertical Shift
1:10 How to Find Amplitude
1:30 Deciding Whether to Use Sine or Cosine
1:40 Parent Function Graphs for Sine and Cosine
2:01 How to Calculate the Period
2:27 Formula for Calculating the Period
2:58 Representing the Graph as a Reflected Cosine Equation
3:37 Representing the Graph with a Sine Equation
4:22 Representing the Graph with a Reflected Sine Equation
4:56 Representing the Graph with a Shifted Cosine Equation
Related Videos:
Graphing Sin and Cos
• Graphing Sin and Cos
Finding a Sinusoidal Equation Given a Maximum and a Minimum
• Finding a Sinusoidal E...
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It's currently 12:44am, and you sir have just saved me. You will never know how grateful I am for this video lol!

[@MariosMathTutoring]

Glad my video helped you SJM!

[@disappointment8094]

12:09am, haha!

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Lmfao 3:08 am

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12:55 am on my end 😅

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12:04am here lol

[@anniquequarlesvanufford5813]

Well, guess who just saved me from failing my trig exam! My teacher tried to explain this but it never made sense till this video!

[@lionel8303]

You deserve the best teacher, just saved me from confusion.

[@emilyt7534]

Thank you so much! Watched about five videos before this and none of them explained this concept as well as you. So glad that I found your channel!

[@Punicia]

Thank you Mario. This is the only video that actually helped me with this topic. I appreciate your ability to make the concept very clear when my teacher can't. +1

[@passionatepro5322]

ITS 7:50 IN THE NIGHT AND YOU SIR HAVE JUST SAVED ME. YOU WILL NEVER KNOW HOW GRATEFUL I AM FOR THIS VIDEO LOL

[@AnnetteCompean]

Dude you just helped me so much! Thank you our teacher didn’t really explain this at all!! he gave us one problem and told us to learn from that!!

[@ArnobDas-q6l]

Thank you so much. You save me from one hour long class rn.

[@MariosMathTutoring]

You're welcome! Glad to help!

[@98567215]

Thank you Mario! Your explanation is very clear and simple.

[@MariosMathTutoring]

You're welcome, glad you found it helpful!

[@MusanGreen]

You are a born teacher. Thank you so much for all your efforts and dedication.

[@MariosMathTutoring]

You are very welcome

[@shashwatpriyadarshi972]

Sir even though Iam a doctor and not a student of mathematics then also I could make sense of it ,that just goes to show what a great teacher you are. Some stupid questions from this doctor- Why are waves represented as sine or cosine functions? Use of integral and differential equations in practical life

[@DrLiangMath]

Your explanation was so systematic, clear and easy to understand. Thanks👍

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I WISH YOU WEALTH

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My math test is next period, and thank you so much for saving me to relieve some stress!

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Thank you so much this helped me understood the most confusing thing my teacher tried to teach us

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You make things so easy to understand thank you

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Thank you so much !!! I got itttttt

[@MariosMathTutoring]

Great job!

[@SWE.Major.TypeError]

Life saver. Thank you, Mario!

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Wow, never knew Johnny Sin is a good mathematics teacher.

[@Olivia-sy8go]

Thank you SO much I was struggling so much with this and you made everything click!

[@temsters8806]

Thank you brother I spent 30 mins on this i was so lost

[@MariosMathTutoring]

Glad it helped!

[@luisv8887]

Mario always bringing great helpful videos thanks Mario!

[@FreshBeatles]

THANK YOU

[@AlexSchmidt-w5y]

I hope this message finds you well. I've been following your KZbin math tutorials and find them incredibly helpful. I have a few questions and was wondering if you could guide me on how best to contact you for some questions. If possible?

[@MariosMathTutoring]

Cool, thanks!

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Thank you so much! Helping me prep for finals!

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mario’s a real one 💯

[@Zoey_Xian]

really really helpful, thank u so much!!!

[@MariosMathTutoring]

Glad it helped!

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Thank you Mario, you are so awesome!

[@leisureacc1186]

Currently 4 min until my test thansk bro

[@kaveenchandra8009]

May God bless you sir

[@waffleisnice]

Wow. Thank you so much, you made it so simple

[@MariosMathTutoring]

You’re welcome! Glad it helped!

[@alwysrite]

Very good explanation

[@MariosMathTutoring]

Glad you liked my video.

[@squidward3089]

Thanks you so much for this video

[@aavasapkota]

Thank you so much!! This was so helpful :D

[@MariosMathTutoring]

You’re welcome Aava!

[@gabii_ella]

saving me for my pop quiz. thank you

[@MariosMathTutoring]

You’re welcome!

[@pedrosan9179]

that really did help a lot thank you

[@MariosMathTutoring]

You’re welcome Pedro!

[@kaylasvegas4660]

great video! thank you!

[@azozvn7014]

Thank u sooooo much you saved my life i will always be grateful to you

[@MariosMathTutoring]

You’re welcome! Glad my videos have helped you!

[@curtpiazza1688]

Excellent!

[@maryangutierrez5878]

can you please explain to me how one can tell if the a value (amplitude) is negative or positive?

[@achyutreddy2007]

From my knowledge, the amplitude is always positive. It's the value of the highest point on the graph subtracted from the midpoint.

[@maryangutierrez5878]

@@achyutreddy2007 i didn’t need this anymore, but thank you so much😭

[@TreSwayy]

I'm learning this on Khan Academy and it's so confusing. I find myself in circles where I do understand then i'll just get randomly stumped.

[@mel0ntttt]

Thank you so much this video is super helpful!

[@honestman276]

Thanks. From Bangladesh.

[@Ro_Show]

Oh my god this saved my grade 🙏. Question however, if you use a positive amplitude on the cosine graph which you did, doesnt that mean that B would be -2pi? Because you said we could use any point when using that one, because it isn’t reflected.

[@Ro_Show]

I mean if you use the maximum on the right instead of the left.**

[@Raabit4g]

Thank you sir,I am from india

[@rseesr7743]

nice video，learning this now. thanks

[@MariosMathTutoring]

Thanks! Glad my video is helping you.

[@counkoganjun]

thanks mario :3

[@MariosMathTutoring]

You’re welcome. Thanks for being part of the channel.

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I really appreciate that you shoot this video! I'm gonna subscribe your channel!!

[@MariosMathTutoring]

Awesome! Glad you liked my video! Welcome to the channel!

[@usmanrasheed1749]

Brilliant dude you always teaches me something.

[@MariosMathTutoring]

Glad my video helped you Usman!

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[@cindychong3562]

wishing my teacher could teach thank you so muchchchchch

[@MariosMathTutoring]

Glad my sine and cosine video helped you Cindy!

[@michellemartinez6375]

Thank you very much !

[@MariosMathTutoring]

You’re welcome Michelle!

[@ngozi8704]

Why is Pi used? I see it in every video and I’m so confused on what to do

[@vasiliibogdan1291]

Hello, do you know how to make it cut off, say from -pi to pi/2 only portion? Thank you!

[@vasiliibogdan1291]

oh nevermind, its just X value

[@mrbloxcraft5611]

Perfection.

[@yashkirdak8805]

How can I share my question to you sir

[@ElectricPeaPlayz]

What about given points?

[@unknown-fd1yz]

Thank you ...

[@MariosMathTutoring]

You’re welcome!

[@samgill2025]

Thankyou

[@MariosMathTutoring]

You’re welcome Simar!

[@juantuthree357]

What does “reflected over the x-axis” mean? Anyone?

[@liyajohnson7405]

if a point is reflected over x axis then the x coordinate remains the same but the sign of y coordinate becomes negative. or simply imagine it as a water image of something with respect to the x axis or it gets flipped over the x axis.

[@jollyelmroot]

Sine starts at origin Cosine starts at maximum

[@aadilmiller3899]

well explained sir, but unfortunately I'm having some sort of deficalty with sin and cosine phase shift. this is one of the problems that i'm finding complicated, 3 sin(2x-pi)+2 i can actually find its amplitude, vertical shift and period, I'm just not getting 'WHY' i need to factor out 2 like this ' 2(x-pi/2)' , why can't i just shift the graph by 'pi' unit to the right..?? again, i can figure out all except it's phase shift i would just like some explanation behind that 'factoring out 2' thing, sorry for this long question. ''please some explanation would be helpfull, I'm struggling with it from last 5 days''

[@MariosMathTutoring]

Aadil, you can shift the graph right pi and then horizontally compress the graph by dividing the x values by 2 however it is easier to factor out the two and calculate the period as pi/2 and then shift that graph right pi/2...either way you will get the same graph...I recommend reviewing transformations of parent functions ....hope that helps

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[@yashkirdak8805]

I have one question

[@MariosMathTutoring]

Graphing Sine and Cosine Functions with Transformations (Multiple Examples) kzbin.info/www/bejne/i2TOpZ2egLeXpMk

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impossible

[@MariosMathTutoring]

Which part?

[@boballos7879]

thank you

[@MariosMathTutoring]

You're welcome