Graphing Cosine with Period Change and Phase Shift

👉 Learn how to graph a cosine function. To graph a cosine function, we first determine the amplitude (the maximum point on the graph), the period (the distance/time for a complete oscillation), the phase shift (the horizontal shift from the parent function), the vertical shift (the vertical shift from the parent function) and the x-scale (the distance between the turns and the x-intercepts). After we have obtained these features, we plot the points on the graph and graph accordingly.

Organized Videos:
✅ How to Graph Trigonometric Functions
✅ How to Graph Tangent | Learn About
✅ How to Graph Secant | Learn About
✅ How to Graph Sine and Cosine | Learn About
✅ How to Graph Trigonometric Functions | Learn About
✅ How to Graph The Sine Function
✅ How to Graph The Cosine Function
✅ How to Graph The Tangent Function
✅ How to Graph The Cotangent Function
✅ How to Graph Cosecant Function
✅ How to Graph The Secant Function

Connect with me:

#trig #graphing #brianmclogan

[teruelryanpaul]

I can't entirely express how thankful I am for this man's commitment to his youtube channel.

[muayadaziz]

Mr. McLogan, you are really extremely interesting math teacher.

[errorcodex]

spent the last who knows how long staring at my hw not quite getting how to get the phase shift right and how to graph the more complex sine graphs and cos graphs. This cleared it up a bunch, i was missing the phase shift equation and the start and end equations made things a lot easier. Thanks!

[shortsbyjim]

Thanks Brian   the way you explain math is amazing

[-smp-scientificmethodpersp]

That calculating for how to keep going on negative pi actually helped. Thanks

[kingofeextv]

I truly understand his videos thank u lods Mclogan💖💗

[usamamuta-ali]

This was the greatest, most understandable explanation on YouTube...! Students around the world appreciate you Mr.McLogan...!

[adrienneferguson]

why did you set the equation that gives you the end point to 2 pie, if the period is only pie?

[Dano-dnwb]

I wish the interval points weren’t so generic. That’s the only possible thing you can struggle with on these problems once you memorize the steps

[sethrigsby]

Would the graphs y = -sin(x) and y = sin(-x) be the same graph? I've looked up each one, and that's what I've found. I wasn't sure if that is correct though, because in Precal Algebra, a negative on the outside of the parentheses affecting the entire function would be completely different than a negative on the inside of the parentheses that is directly affecting the x values. I'm assuming that in Trig we don't reflect across the y-axis?

[TheOneTrite]

So in this problem you added pi inside the cosine function. What I am confused about is how come the function shifts (pi/2) to the left instead of pi to left?

[ЯКАРТОФЕЛЬ]

How did you get -pi/2 at the starting point and pi/2 at the end point?

[alfonsomiguelantonio]

is pi/4 automatically the x scale? always?

[hayderdheyaa]

Mr.Mclogan why u didn’t reflect the graph ?

[Orangematz]

When you used the trick of setting whatever in the parenthesis equal to both 0 and 2pi, it didn't seem to work for this problem.

y=4cos(3x+6pi)-2

The start (equal to 0) worked (solvedto 2pi), but the end (equal to 2pi) I got 4pi/3, which wasn't right (8pi/3 should have been the end of the initial period). Any thoughts on what I may be doing wrong?

[godslittlegirl]

Wait....
Why didn't the graph move up by pi?

[allistermi]

Why critical points always use period divided by four? Why it is four?

[chikahantime]

how did u get a 4 in pie over 4? sorry, im not good in math.

[amritasarker]

why did you set the end of the function to 2 pi?