How do I plot a graph with the grid for trig functions with 0 ≤ x ≤ 2π

y1 = cos (x) ... solid line, red, no marker

y2 = -sin (x) ... dashed line, blue, no marker

y3 = cos (x)’ ... no line, blue, circle

Cos(x)' is the ferivative of cos(x)

Answer 1

[John D'Errico]

@Sean

syms x
f = cos(x)

f = 

dfdx = diff(f)

dfdx = 

help fplot

 fplot - Plot expression or function
    This MATLAB function plots the curve defined by the function y = f(x)
    over the default interval [-5 5] for x.

    Syntax
      fplot(f)
      fplot(f,xinterval)

      fplot(funx,funy)
      fplot(funx,funy,tinterval)

      fplot(___,LineSpec)
      fplot(___,Name,Value)
      fplot(ax,___)
      fp = fplot(___)
      [x,y] = fplot(___)

    Input Arguments
      f - Function to plot
        function handle
      xinterval - Interval for x
        [–5 5] (default) | two-element vector of form [xmin xmax]
      funx - Parametric function for x coordinates
        function handle
      funy - Parametric function for y coordinates
        anonymous function | function handle
      tinterval - Interval for t
        [-5 5] (default) | two-element vector of form [tmin tmax]
      ax - Axes object
        axes object
      LineSpec - Line style, marker, and color
        string scalar | character vector

    Name-Value Arguments
      MeshDensity - Number of evaluation points
        23 (default) | number
      Color - Line color
        [0 0.4470 0.7410] (default) | RGB triplet | hexadecimal color code |
        "r" | "g" | "b" | ...
      LineStyle - Line style
        "-" (default) | "--" | ":" | "-." | "none"
      LineWidth - Line width
        0.5 (default) | positive value
      Marker - Marker symbol
        "none" (default) | "o" | "+" | "*" | "." | ...
      MarkerEdgeColor - Marker outline color
        "auto" (default) | RGB triplet | hexadecimal color code | "r" |
        "g" | "b" | ...
      MarkerFaceColor - Marker fill color
        "none" (default) | "auto" | RGB triplet | hexadecimal color code |
        "r" | "g" | "b" | ...
      MarkerSize - Marker size
        6 (default) | positive value

    Output Arguments
      fp - One or more FunctionLine or ParameterizedFunctionLine objects
        scalar | vector

    Examples
      openExample('graphics/PlotExpressionExample')
      openExample('graphics/PlotParametricCurveExample')
      openExample('graphics/SpecifyPlottingIntervalAndPlotPiecewiseFunctionsExample')
      openExample('graphics/SpecifyLinePropertiesAndDisplayMarkersExample')
      openExample('graphics/ModifyPlotAfterCreationExample')
      openExample('graphics/PlotMultipleLinesInSameAxesExample')
      openExample('graphics/AddTitleAndAxisLabelsAndFormatTicksExample')

    See also fcontour, fmesh, fplot3, fsurf, hold, title, fimplicit,
      FunctionLine Properties, ParameterizedFunctionLine Properties

    Introduced in MATLAB before R2006a
    Documentation for fplot
       doc fplot

    Other uses of fplot

       symbolic/fplot

Answer 2

[Sam Chak]

Hi @Sean

You have likely not yet looked up the plot() function. There are several examples.

help plot

 plot - 2-D line plot
    This MATLAB function creates a 2-D line plot of the data in Y versus the
    corresponding values in X.

    Vector and Matrix Data
      plot(X,Y)
      plot(X,Y,LineSpec)
      plot(X1,Y1,...,Xn,Yn)
      plot(X1,Y1,LineSpec1,...,Xn,Yn,LineSpecn)
      plot(Y)
      plot(Y,LineSpec)

    Table Data
      plot(tbl,xvar,yvar)
      plot(tbl,yvar)

    Additional Options
      plot(ax,___)
      plot(___,Name,Value)
      p = plot(___)

    Input Arguments
      X - x-coordinates
        scalar | vector | matrix
      Y - y-coordinates
        scalar | vector | matrix
      LineSpec - Line style, marker, and color
        string scalar | character vector
      tbl - Source table
        table | timetable
      xvar - Table variables containing x-coordinates
        string array | character vector | cell array | pattern |
        numeric scalar or vector | logical vector | vartype()
      yvar - Table variables containing y-coordinates
        string array | character vector | cell array | pattern |
        numeric scalar or vector | logical vector | vartype()
      ax - Target axes
        Axes object | PolarAxes object | GeographicAxes object

    Name-Value Arguments
      Color - Line color
        RGB triplet | hexadecimal color code | "r" | "g" | "b" | ...
      LineStyle - Line style
        "-" (default) | "--" | ":" | "-." | "none"
      LineWidth - Line width
        0.5 (default) | positive value
      Marker - Marker symbol
        "none" (default) | "o" | "+" | "*" | "." | ...
      MarkerIndices - Indices of data points at which to display markers
        1:length(YData) (default) | vector of positive integers |
        scalar positive integer
      MarkerEdgeColor - Marker outline color
        "auto" (default) | RGB triplet | hexadecimal color code | "r" |
        "g" | "b" | ...
      MarkerFaceColor - Marker fill color
        "none" (default) | "auto" | RGB triplet | hexadecimal color code |
        "r" | "g" | "b" | ...
      MarkerSize - Marker size
        6 (default) | positive value
      DatetimeTickFormat - Format for datetime tick labels
        character vector | string
      DurationTickFormat - Format for duration tick labels
        character vector | string

    Examples
      openExample('graphics/CreateLinePlotExample')
      openExample('graphics/PlotMultipleLinesExample')
      openExample('graphics/CreateLinePlotFromMatrixExample')
      openExample('graphics/SpecifyLineStyleExample')
      openExample('graphics/SpecifyLineStyleColorAndMarkerExample')
      openExample('graphics/DisplayMarkersAtSpecificDataPointsExample')
      openExample('graphics/SpecifyLineWidthMarkerSizeAndMarkerColorExample')
      openExample('graphics/AddTitleAndAxisLabelsExample')
      openExample('matlab/SpecifyDurationTickFormatsExample')
      openExample('graphics/PlotTableDataExample')
      openExample('graphics/PlotTableMutliVariablesExample')
      openExample('graphics/PlotSpecifyAxes19bExample')
      openExample('graphics2/ChangeLinePropertiesUsingHandlesExample')
      openExample('graphics/PlotCircleExample')

    See also title, xlabel, ylabel, xlim, ylim, legend, hold, gca, yyaxis,
      plot3, loglog, Line Properties

    Introduced in MATLAB before R2006a
    Documentation for plot
       doc plot

    Other uses of plot

       AggregateBayesianOptimization/plot
       alphaShape/plot
       antenna.Circle/plot
       backscatterBicyclist/plot
       backscatterPedestrian/plot
       Battery.Parameters/plot
       Battery.Pulse/plot
       Battery.PulseSequence/plot
       BayesianOptimization/plot
       blm/plot
       cfit/plot
       cgdatasetnode/plot
       cgrules/plot
       cgv.CGV/plot
       climateScenario/plot
       clusterDBSCAN/plot
       clustergram/plot
       clustering.evaluation.CalinskiHarabaszEvaluation/plot
       comm.MemorylessNonlinearity/plot
       comm.Ray/plot
       conjugateblm/plot
       cornerPoints/plot
       customblm/plot
       cylinderModel/plot
       DataMatrix/plot
       diffuseblm/plot
       digraph/plot
       driving.heremaps.LaneTopology/plot
       driving.Path/plot
       drivingScenario/plot
       dtree/plot
       empiricalblm/plot
       esbacktest/plot
       eyeMask/plot
       fairnessMetrics/plot
       frd/plot
       graph/plot
       HeatMap/plot
       iddata/plot
       idnlarx/plot
       idnlhw/plot
       imageviewset/plot
       InflationCollisionChecker/plot
       KAZEPoints/plot
       laneBoundarySegment/plot
       lassoblm/plot
       LayerGraph/plot
       LeastSquaresResults/plot
       lidarScan/plot
       lime/plot
       LinearModel/plot
       localavfit/plot
       localmod/plot
       localmulti/plot
       matlab.buildtool.Plan/plot
       mixconjugateblm/plot
       mixsemiconjugateblm/plot
       monovslam/plot
       mpc/plot
       MSERRegions/plot
       NLMEResults/plot
       ntree/plot
       opc.hda.Data/plot
       opticalFlow/plot
       parkingSpace/plot
       pathPlannerRRT/plot
       pcviewset/plot
       phased.FMCWWaveform/plot
       phased.LinearFMWaveform/plot
       phased.MFSKWaveform/plot
       phased.PhaseCodedWaveform/plot
       phased.RectangularWaveform/plot
       phased.SteppedFMWaveform/plot
       phytree/plot
       polyshape/plot
       prob.NormalDistribution/plot
       propagationData/plot
       pulseWaveformLibrary/plot
       reidentificationmetrics/plot
       RepeatedMeasuresModel/plot
       rfchain/plot
       rgbdvslam/plot
       roadrunnerHDMap/plot
       rocmetrics/plot
       scenariobuilder.ActorTrackData/plot
       scenariobuilder.GPSData/plot
       scenariobuilder.Trajectory/plot
       semiconjugateblm/plot
       sfit/plot
       shapley/plot
       SimBiology.fit.ParameterConfidenceInterval/plot
       SimBiology.fit.PredictionConfidenceInterval/plot
       SimBiology.gsa.ElementaryEffects/plot
       SimBiology.gsa.MPGSA/plot
       SimBiology.gsa.Sobol/plot
       simscape.logging.Node/plot
       simscape.logging.Series/plot
       simscape.logging/plot
       Simulink.sdi.DatasetRef/plot
       Simulink.sdi/plot
       Simulink.SimulationData.Parameter/plot
       slrealtime.ProfilerData/plot
       stereovslam/plot
       sweepset/plot
       tall/plot
       tcnDetector/plot
       timeseries/plot
       tireData/plot
       tireModel/plot
       trajectoryErrorMetrics/plot
       umargin/plot
       varbacktest/plot
       vehicleCostmap/plot
       wdectree/plot
       xregmodel/plot
       xregtransient/plot
       xregtwostage/plot

[Sean]

I have used the plot() function some I am trying to figure out how to

plot the dreviative of cos(x) or cos(x)'

while I know I can just use

x = 0:pi/100:2*pi;

y = -sin(x)

plot(x,y1,'-r',x,y2,'--b',x,y3,'o b')

because cos(x)' = -sin(x)

I am tring to use matlab to solve the for the derivative of cosine

I fould this formula for finding the dervative but I don't think it is goign to be useful

dcos( X)/ dx = -sin(x)

[Sam Chak]

Thanks for your clarification. If this is a routine exercise to obtain the derivative of a trig function, you can use the symbolic approach as demonstrated in @John D'Errico's answer. Otherwise, you can use the numerical approach:

x   = -pi:0.001:pi;
y   = cos(x);
dy  = gradient(y)./gradient(x);
plot(x, [y; dy])

[Sean]

thank you, for the response both the symbolic aproach and numerical aproach are helpful!