1. There's really nothing special about how I remember transformations. However, there is a step by step process that I follow when I need to graph them. The first thing I do is find the original graph (by removing the transformations) and in my head, I picture how the graph looks. After that I start to add in the transformations as I go.
- when a number greater than 1 is in front of the x [ex. cos 3x] then the input will be multiplied and the whole graph will shrink on the x-axis.
-when a fraction is in front of the x [ex. cos 1/2 x] then the input will be reduced and the whole graph will expand on the x-axis.
[[This affects the period of the graph]]
-when any number is subtracted from the input and is in parenthesis, then it will shift the graph to the right.
-when any number is added to the input and is in parenthesis, then it will shift to the left.
-when any number is subtracted from the input and is NOT in parenthesis, then it will shift down. -when any number is added to the input and is NOT in parenthesis, then it will shift up.
2. How I remember trigonometry is much easier. If I need to find an angle, lets say sin 1/2, all I have to do is remember on what quadrant sin is positive. Then I think back to the unit circle and remember when sin (Y) is equal to 1/2. After all that, I find out the angle is equal to pie/6 and 5pie/6.
A neat trick that I know for remembering the positive values in the unit circle is "ALL STUDENTS TAKE CALCULUS"
In quadrant I: ALL of the values are positive.
In quadrant II: Sine is positive
In quadrant III: Tangent is positive (-sin x/-cos x)
In quadrant IV: Cosine is positive.
3. What doesn't really confuse me but does worry me about trigonometry are the sec -(x), csc-(x), and cot-(x) graphs. They are still not well engraved in my head.
-when a fraction is in front of the x [ex. cos 1/2 x] then the input will be reduced and the whole graph will expand on the x-axis.
[[This affects the period of the graph]]
-when any number is subtracted from the input and is in parenthesis, then it will shift the graph to the right.
-when any number is added to the input and is in parenthesis, then it will shift to the left.
-when any number is subtracted from the input and is NOT in parenthesis, then it will shift down. -when any number is added to the input and is NOT in parenthesis, then it will shift up.
2. How I remember trigonometry is much easier. If I need to find an angle, lets say sin 1/2, all I have to do is remember on what quadrant sin is positive. Then I think back to the unit circle and remember when sin (Y) is equal to 1/2. After all that, I find out the angle is equal to pie/6 and 5pie/6.
A neat trick that I know for remembering the positive values in the unit circle is "ALL STUDENTS TAKE CALCULUS"
In quadrant I: ALL of the values are positive.
In quadrant II: Sine is positive
In quadrant III: Tangent is positive (-sin x/-cos x)
In quadrant IV: Cosine is positive.
3. What doesn't really confuse me but does worry me about trigonometry are the sec -(x), csc-(x), and cot-(x) graphs. They are still not well engraved in my head.
Oh yeah! Ms. Gapac's little mnemonic device. Is that how that's spelled? XD
ReplyDeleteDo not you worry, my friend! Those graphs are not there because we haven't learned them before until now. Soon enough they will be! x]
i dont think you can do much about sec -(x), csc-(x), and cot-(x) graphs. just look at them a lot and try to remember. :)
ReplyDeletenice job spelling cynthia, nice job on the tips rocio!
ReplyDelete