C HAPTER 7: T RIGONOMETRIC G RAPHS 7.2: G RAPHS OF THE C OSECANT, S ECANT, AND C OTANGENT F UNCTIONS Essential Question: How do the graphs of csc, sec and cot relate to their inverse functions?

7-2: G RAPHS OF C SC /S EC /C OT The Cosecant Function Because sin t and csc t are reciprocals, the curves meet at the same peaks, they just go in opposite directions. The graph of csc t is undefined wherever sin t would equal 0 Red = sin t Blue = csc t

7-2: G RAPHS OF C SC /S EC /C OT The Secant Function The sec/cos graphs behave just like the csc/sin graphs. The graph of sec t is undefined wherever cos t would equal 0 Red = cos t Blue = sec t

7-2: G RAPHS OF C SC /S EC /C OT The Cotangent Function Looks just like the tangent function, only flipped horizontally. Why? The graph of cot t is undefined wherever tan t would equal 0, meaning its undefined at each interval of π Red = tan t Blue = cot t

7-2: G RAPHS OF C SC /S EC /C OT Reflection and Vertical Stretches Graph -3 csc t Use the reciprocal graph: -3 sin t Take that graph, and flip the curves Red = -3 sin t Blue = -3 csc t

7-2: G RAPHS OF C SC /S EC /C OT Vertical Stretch and Vertical Shift Graph 2 sec t – 3 Use the reciprocal graph: 2 cos t – 3 Take that graph, and flip the curves Red = 2 cos t – 3 Blue = 2 sec t – 3

7-2: G RAPHS OF C SC /S EC /C OT Reflection, Vertical Stretch, and Horizontal Shift Graph -3 cot(t – π / 4 ) Take the parent function: cot t, which is the reciprocal of tan t Shift it π / 4 units to the right Flip it vertically Stretch it by a factor of 3 tan t cot t cot( t – π / 4 ) -cot( t – π / 4 ) -3cot( t – π / 4 )

7-2: G RAPHS OF C SC /S EC /C OT Assignment Page 490 – 491 Problems 1 – 17, odd