#graphing trig

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31.2

Cosine (cos)

Parent f(x)

Sibling Graphs

Sine and Cosine graphing method is the same aside from the y-value set up.

View this for trig graphing basics.

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Graphing and Writing Trigonometric Functions

On This Page: Reference formula Graphing transformations of sine Graphing transformations of cosine Graphing transformations of tangent Writing two different equations for sine/cosine

Reference Formula Just like regular transformations in the form of y = af(b(x - c)) + d, except f would be labelled sin, cos or tan.

Graph the following: -2sin3(x - π) + 5 Start with the basic graph of y = sinx

Use the key points to y = sinx to transform the starter graph. y = sinx (0,0) (π/2,1) (π,0) (3π/2,-1) (2π,0) y = -2sinx (multiplying y-coordinate by -2) (0,0) --> (0,0) (π/2,1) --> (π/2,-2) (π,0) --> (π,0) (3π/2,-1) --> (3π/2,2) (2π,0) --> (2π,0) y = -2sin3x (dividing x-coordinate by 3) (0,0) --> (0,0) (π/2,-2) --> (π/6,-2) (π,0) --> (π/3,0) (3π/2,2) --> (π/2,2) (2π,0) --> (2π/3,0) Graph how it looks now.

Now apply the translations. y = -2sin3(x - π) (adding π to x-coordinate) (0,0) --> (π,0) (π/6,-2) --> (7π/6,-2) (π/3,0) --> (4π/3,0) (π/2,2) --> (3π/2,2) (2π/3,0) --> (5π/3,0) y = -2sin3(x - π) + 5 (adding 5 to y-coordinate) (π,0) --> (π,5) (7π/6,-2) --> (7π/6,3) (4π/3,0) --> (4π/3,5) (3π/2,2) --> (3π/2,7) (5π/3,0) --> (5π/3,5) Graph the final graph.

Graph the following: -cos2(x + π/2) - 3 Start with the basic graph of y = cosx

Use the key points to y = cosx to transform the starter graph. y = cosx (0,1) (π/2,0) (π,-1) (3π/2,0) (2π,1) y = -cosx (multiplying y-coordinate by -1) (0,1) --> (0,-1) (π/2,0) --> (π/2,0) (π,-1) --> (π,1) (3π/2,0) --> (3π/2,0) (2π,1) --> (2π,-1) y = -cos2x (dividing x-coordinate by 2) (0,-1) --> (0,-1) (π/2,0) --> (π/4,0) (π,1) --> (π/2,1) (3π/2,0) --> (3π/4,0) (2π,-1) --> (π,-1) Graph how it looks now.

Now apply the translations. y = -cos2(x + π/2) (subtracting π/2 from x-coordinate) (0,-1) --> (-π/2,-1) (π/4,0) --> (-π/4,0) (π/2,1) --> (0,1) (3π/4,0) --> (π/4,0) (π,-1) --> (π/2,-1) y = -cos2(x + π/2) - 3 (subtract 3 from y-coordinate) (-π/2,-1) --> (-π/2,-4) (-pi/4,0) --> (-π/4,-3) (0,1) --> (0,-2) (π/4,0) --> (π/4,-3) (π/2,-1) --> (π/2,-4) Graph the final graph.

Graph the following: y = tan2(x - π/2) + 1 Start with the basic graph of y = tanx

Use y = tanx's zeros and asymptotes. y = tanx (0,0) (π,0) (2π,0) x /= π/2 x /= 3π/2 y = tan2x (dividing x-coordinate by 2) (0,0) --> (0,0) (π,0) --> (π/2,0) (2π,0) --> (π,0) x /= π/2 --> x /= π/4 x /= 3π/2 --> x /= 3π/4 Graph how it looks now.

Now apply the translations. y = tan2(x - π/2) (adding π/2 to x-coordinate) The graph would still look the same. After applying the final translation, the final graph should look like this:

Determine the equation of this graph in the form of a sine function and cosine function.

For sine: Divide it by its period and work from there on. y = -sinx For cosine: Divide it by its period and work from there on. y = cos(x + π/2)