7/27/2019 Math 125 - Guidelines for Sketching Graphs of Sine and Cosine Functions

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Guidelines for Sketching Graphs of Sine and Cosine FunctionsTo graph y = A sin(x) or y = A cos(x), with > 0, follow these

steps:

Step 1: Use the amplitude to determine that maximum and minimumvalues of the function.

Step 2: Find the period, . Then divide the interval [0,

] into

four equal subintervals.

a)Find the midpoint of the interval by adding the x-valuesof the endpoints and dividing by 2.

b)Find the midpoints of the two subintervals found in a),using the same procedure.

Step 3: Make the table of these subintervals to obtain five keypoints on the graph.Step 4: Connect these points with a sinusoidal graph to obtain thegraph of one circle and extend the graph in each direction

to make it complete.

Guidelines for Sketching Graphs of Tangent and Cotangent FunctionsTo graph y = A tan(x) or y = A cot(x), with > 0, follow these

steps:

Step 1: Find the period,

Step 2: To locate two adjacent vertical asymptotes, solve thefollowing equations for x

a)For y = A tan(x): x =

and x =

b)For y = A cot(x): x = 0 and x = Step 3: Divide the interval formed by the vertical asymptotes into

four equal lengths.

a)Find the midpoint of the interval by adding the x-valuesof the endpoints and dividing by 2.

b)Find the midpoints of the two subintervals found in a),using the same procedure.

Step 4: Make the table for the first-quarter point, midpoint, andthird-quarter point, using the x-values found in Step 3.

Step 5: Connect the points and extend the graph in each directionto make it complete.

7/27/2019 Math 125 - Guidelines for Sketching Graphs of Sine and Cosine Functions

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Guidelines for Sketching Graphs of Secant and Cosecant FunctionsTo graph y = A sec(x) or y = A csc(x), with > 0, follow these

steps:

Step 1: Graph the corresponding reciprocal function as a guide,using dashed curve

To graph Use as a guidey = A sec(x) y = A cos(x)

y = A csc(x) y = A sin(x)

Step 2: Sketch the vertical asymptotes.They will have equations of the form x = k, where k in an

x-intercept of the graph of the guide function.

Step 3: Sketch the graph of the desired function by drawing thetypical U-shaped branches between the adjacent asymptotes.

The branches will be above the graph of the guide function

when the guide function values are positive and below the

graph of the guide function when the guide function values

are negative.

Further Guidelines for Sketching Graphs of the Sine and CosineFunctions.Step 1: Fine an interval whose length is one period

by solving

the three-part inequality 0 x - 2

Step 2: Divide the interval into four equal lengthsStep 3: Make the table to find 5 key pointsStep 4: Connect the points