way more fun the sine and cosine CscΘ and SecΘ Graphs way more fun the sine and cosine

CscΘ??? How can we find cscΘ? Use your table of values to plot the cscΘ function.

Looking at the Sine Graph Look at your worksheet from last week for sine’s key points

What we know about csc Cscϴ = 1/sinϴ

Use sine values to get the following: csc(0°) = ____0_____ csc(45°) = _2/√2 =√2 csc(90°) = ___1___ csc(135°) = _2/√2 =√2 csc(180°) = undefined csc(270°) = ___-1___ csc(360°) = undefined csc(1°) = ____57.3_ csc(179°) = 57.3 csc(181°) = __-57.3_ csc(359°) = __-57.3_

In general: asymptotes = 180°n Every 180 degrees Where do they go? What do they mean? 0°180°360° In general: asymptotes = 180°n Every 180 degrees Where the graph cannot occur. There are no outputs at those points.

Use the graph and what you know about the sine graph to complete the following:   Period: 360 or 2π With transformations:360/b or 2π/b Vertical Asymptotes: x = nπ = n180° Maximums: (270, -1) -Where minimums were Minimums: (90,1) - Where maximums were Where sine or cosine was 0 At multiples of 180°

Let’s see it Csc Graph Sine and Csc Graphs Make sure to click on the links in pale blue above (there are two) – use the sliders to adjust the values and see how the transformations and translations affect the parent graphs

To graph cosecant graphs: First graph the sine graph with the transformations (just as we did in the last section). Put asymptotes where the sine graph was zero Put maximums where the sine graph had minimums Put minimums where the sine graph had maximums

Examples Try the example on the back of the first page at this time – graph the sine and cosine graphs and go from there!

SecΘ???? How can we find secΘ? Use your table of values to plot the secΘ function.

Looking at the Cosine Graph Cosine Key Points: ( , ), ( , ), ( , ), ( , ), ( , )

What we know about sec secϴ = 1/cosϴ

No output value at those x-values At x = 90 + 180n At x = π/2 +πn Asymptotes Where are they? What do they mean? No output value at those x-values At x = 90 + 180n At x = π/2 +πn Starting at 90 and every 180 after that

Let’s See It Make sure to click on the links in pale blue below(there are two) – use the sliders to adjust the values and see how the transformations and translations affect the parent graphs http://www.analyzemath.com/Secant/Secant.html secant

To graph secant graphs: First graph the cosine graph with the transformations (just as we did in the last section). Put asymptotes where the cosine graph was zero Put maximums where the cosine graph had minimums Put minimums where the cosine graph had maximums

Examples Try the example on the back of the first page at this time – graph the sine and cosine graphs and go from there!