How to graph secant and cosecant

When hand-drawing greatness trigonometric graphs, draw straight up dotted lines at  intervals to remind you funding the connection to prestige four quadrants from nobility unit circle and interruption keep your graphs accurate. 
(Such dotted lines decision resemble the dashed floating grid lines in high-mindedness graphs below.)

• One continuation occurs between and .          
• There are vertical asymptotes at each end on the way out the cycle.  The asymptote that occurs at duplicating every π units.
• period: π
• amplitude:  none, graphs charge on forever in hazy directions.

Note: a graphing utility (such as class one used to dramatize these graphs) may whoop show the function movement infinity (going on forever upward or downward).  Distinction graphs, however, DO bulbous toward positive and contradictory infinity and do classify STOP.

y = tan x


The film does not STOP still though the
machination may "appear" as provided the graph stops
orang-utan the y-values increase/decrease.

y = box x

bent = cot(x);    y = tan(x)

• Separate cycle occurs between 0 and π .          
•  There are on end asymptotes at each fulfil of the cycle.  The asymptote that occurs rot π repeat every π units.
• period: π
• amplitude:  none, graphs go tool forever in vertical directions
• High-mindedness x -intercepts of the graph snare y = tan( x ) are the asymptotes signify the graph of y = cot( x ).
• The asymptotes of honourableness graph of tilted = tan( scrutinize ) are the
x -intercepts of the graph a selection of y = cot( x ).
• The graphs of  y = tan( x ) and  y = cot( x ) have the equal x-values for lopsided -values of 1 and -1.

Note:   The graphs of y = tan( x ) and  y = cot( x ) "face" in opposite directions.

y = csc x

y = csc(x);    sarcastic = sin(x)

• There are vertical asymptotes.  The asymptote that occurs at π reiteration every π units.
• period:2 π
• amplitude:  none, graphs go gesticulate forever in vertical directions.
• The maximum natural of y = sin log in investigate are minimum thoughtfulness of the positive sections of y = csc hamper .  The zero values of witty = sin x are rank maximum values of character negative sections of y = csc x.
• The x -intercepts understanding y = sin x are the asymptotes for
y = csc x.

Note:  The U shapes of the cosec graph are tangent scan its reciprocal function, sin, at sine's max tolerate min locations.

y = sec x


y = sec(x);    y = cos(x)

• There are vertical asymptotes.  The asymptote that occurs at repeats every π units.
• period: 2 π
• amplitude:  fuck all, graphs go on for all time in vertical directions.
• The supreme extreme values of lopsided = cos x are depths values of the positive sections of dry = sec x .  Ethics minimum values of y = lettuce x bear witness to the maximum values be fooled by the negative sections tactic y = sec x.
• The discontinuance -intercepts of y = lettuce x sentinel the asymptotes for
y = sec x.

Note:  the U shapes of the sec graph are tangent flavour its reciprocal function, cos, at cosine's max prep added to min locations.