GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t"...
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Transcript of GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t"...
![Page 1: GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t" chart and let's choose values from our unit circle.](https://reader036.fdocuments.net/reader036/viewer/2022062511/5513ed6955034679748b5a37/html5/thumbnails/1.jpg)
GRAPHS OF OTHER TRIG FUNCTIONS
xxf tan xxf cot
xxf sec xxf csc
![Page 2: GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t" chart and let's choose values from our unit circle.](https://reader036.fdocuments.net/reader036/viewer/2022062511/5513ed6955034679748b5a37/html5/thumbnails/2.jpg)
6
We are interested in the graph of y = f(x) = tan x
Start with a "t" chart and let's choose values from our unit circle and find the tangent values. Tangent has a period of so it will repeat every .
x y = tan x
3
2
undefined
73.13
4
1
6
58.0
3
3
x
y
2
3
2
3
6
would mean there is a vertical asymptote here
![Page 3: GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t" chart and let's choose values from our unit circle.](https://reader036.fdocuments.net/reader036/viewer/2022062511/5513ed6955034679748b5a37/html5/thumbnails/3.jpg)
6
y = tan xLet's choose more values.
x y = tan x
6
0 0
73.13
4
1
3
58.03
3
x
y
2
3
2
3
6
would mean there is a vertical asymptote here
2
undefined
Since we went from we have one complete period 2
to2
![Page 4: GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t" chart and let's choose values from our unit circle.](https://reader036.fdocuments.net/reader036/viewer/2022062511/5513ed6955034679748b5a37/html5/thumbnails/4.jpg)
Let's see what the graph would look like for y = tan x for 3 complete periods.
The vertical lines are not part of the graph but are the asymptotes. If you use your graphing calculator it will probably put those in as well as showing the graph.
![Page 5: GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t" chart and let's choose values from our unit circle.](https://reader036.fdocuments.net/reader036/viewer/2022062511/5513ed6955034679748b5a37/html5/thumbnails/5.jpg)
Transformations apply as usual. Let’s try one.
4tan2
xy
reflect over x-axis
right /4
up 2
xy tan
xy tan
4tan
xy
4tan2
xy
![Page 6: GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t" chart and let's choose values from our unit circle.](https://reader036.fdocuments.net/reader036/viewer/2022062511/5513ed6955034679748b5a37/html5/thumbnails/6.jpg)
Since the period of tangent is , the period of tan x is:
T
xy 2tan The period would be /2
y = tan x
y = tan 2x
![Page 7: GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t" chart and let's choose values from our unit circle.](https://reader036.fdocuments.net/reader036/viewer/2022062511/5513ed6955034679748b5a37/html5/thumbnails/7.jpg)
3
6
What about the graph of y = f(x) = cot x?
This would be the reciprocal of tangent so let's take our tangent values and "flip" them over.
x tan x y = cot x
3
2
undefined
3
4
1
6
3
1
x
y
2
2
3
6
0
58.03
1
1
73.13
![Page 8: GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t" chart and let's choose values from our unit circle.](https://reader036.fdocuments.net/reader036/viewer/2022062511/5513ed6955034679748b5a37/html5/thumbnails/8.jpg)
3
6
x tan x y = cot x
6
0 0
3
4
1
3
3
1
x
y
2
2
3
6
undefined
58.03
1
1
73.13
y = cot xLet's choose more values.
2
undefined 0
We need to see more than one period to get a good picture of this.
![Page 9: GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t" chart and let's choose values from our unit circle.](https://reader036.fdocuments.net/reader036/viewer/2022062511/5513ed6955034679748b5a37/html5/thumbnails/9.jpg)
y = cot x
Again the vertical lines are not part of the graph but are the asymptotes.
Let's look at the tangent graph again to compare these.
Notice vertical asymptotes of one are zeros of the other.
y = tan x
![Page 10: GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t" chart and let's choose values from our unit circle.](https://reader036.fdocuments.net/reader036/viewer/2022062511/5513ed6955034679748b5a37/html5/thumbnails/10.jpg)
For the graph of y = f(x) = csc x we'll take the reciprocals of the sine values.
x sin x y = csc x
6
0 0
2
1
2
1
6
5
When we graph these rather than plot points after we see this, we'll use the sine graph as a sketching aid and then get the cosecant graph.
x
y
1
- 1
undefined
2
1
2
12
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y = f(x) = csc xchoose more values
x sin x y = csc x
6
7 0
2
1
2
31
6
112
1
We'll use the sine graph as the sketching aid.
x
y
1
- 12 0
6
2
undefined
2
1
2
undefined
When the sine is 0 the
cosecant will have an
asymptote.
![Page 12: GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t" chart and let's choose values from our unit circle.](https://reader036.fdocuments.net/reader036/viewer/2022062511/5513ed6955034679748b5a37/html5/thumbnails/12.jpg)
Again the vertical lines are not part of the graph but are where the cosecant is undefined (which is where the sine was 0 although this graphing program seemed to draw them a little to the right. They should cross the x-axis where the sine is 0)
Let's add in the graph of the sine function so you can see how if you graph it, you can then easily use it to graph the cosecant.
Let's look over a few periods at the graph of y = csc x
![Page 13: GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t" chart and let's choose values from our unit circle.](https://reader036.fdocuments.net/reader036/viewer/2022062511/5513ed6955034679748b5a37/html5/thumbnails/13.jpg)
For the graph of y = f(x) = sec x we'll take the reciprocal of the cosine values.
x cos x y = sec x
3
0 1
2
1
2
0
3
22
1
x
y
1
- 1 6
1
2
undefined
2
![Page 14: GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t" chart and let's choose values from our unit circle.](https://reader036.fdocuments.net/reader036/viewer/2022062511/5513ed6955034679748b5a37/html5/thumbnails/14.jpg)
y = f(x) = sec x Choose more values.
x cos x y = sec x
3
4 1
2
1
2
30
3
52
1
Again the cosine graph will help graph the secant graph.
x
y
1
- 1 6
2 1
1
2
undefined
2
1
![Page 15: GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f(x) = tan x Start with a "t" chart and let's choose values from our unit circle.](https://reader036.fdocuments.net/reader036/viewer/2022062511/5513ed6955034679748b5a37/html5/thumbnails/15.jpg)
Again the vertical lines are not part of the graph but are where the secant is undefined (which is where the cosine was 0)
Let's look over a few periods at the graph of y =sec x
Let's add in the graph of the cosine function so you can see how if you graph it, you can then easily use it to graph the secant.