How To Graph Trigonometric Functions | Trigonometry

This trigonometry video tutorial explains how to graph sine and cosine functions using transformations, horizontal shifts / phase shifts, vertical shifts, amplitude, and the period of the sinusoidal function. This video contains many examples and practice problems on graphing trigonometric functions for you to master this topic.
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The full version explains how to graph secant, cosecant, tangent and cotangent functions.

[@TheOrganicChemistryTutor]

Full 1 Hour 25 Minute Video: www.patreon.com/MathScienceTutor Direct Link to The Full Video: bit.ly/38wtIWU

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[@Jmpwfdpdl]

For anyone wondering how he figures out the tick mark values on the x-axis: there are 5 critical points in the sin/cos cycle. Look at a one cycle of a cos/sin graph, and there will be 5 values: 2 values dictating the upper/lower bounds (y-axis values), and 3 values that will cross the x-axis (zeros). In order to find those critical point values (if you're dealing with a phase-shift), you find the value of the phase shift (0=Bx+c, solving for x), and then you add pi/2 recursively. For example, for y=sin(x+pi/3), the graph will start at x=-pi/3. Critical point #1 is -pi/3. To find critical point #2, -pi/3 + pi/2 = pi/6. To find critical point #3, pi/6 + pi/2 = 2pi/3. And so on until you have 5 values. You can use a calculator to add everything to make it easier. if you're still having trouble, google LibreText Mathematics section 2.4 on Phase shift.

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To Sum Up: For equations y=a sin(bx) and y=a cos(bx), |a| is the highest y value point on the graph and -|a| is the lowest y value point on the graph. |b| represents the frequency of the graph or 2pi/b

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I don't get it at the level of 15:15 because of the graph extending to 4pii and why is the negative y-axis is upto -3 .

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Thanks Mr, but that function of y=2cos(x)-1 the period is in 360 degrees, or am I confused.

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How did you get 3pie/2? 19:07

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Mistake at 21:48 it should be 5 pi/2 not 4. Great Video regardless.

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you can also think of B as the number of cycles within a length of 2π

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What's the period of the function y= sin x + cosx???

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[@sambi8074]

At 21:50 the number in between 5 and 1 should be 3 on the y-axis of the graph.

[@BethlehemFetene-gs9ms]

There is 2 at the middle. Its just cause the amplitude is 2 he shifted the graph 2 units up and down from 3 which will bring us to the numbers 5 and 1 respectively.

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at 17:45 isn’t the general form of sine function is asinx(bx-c)+d?

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No it is + c

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how do you know how many key points the graph are that's where I'm having a hard time

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