I have trig test and I have no idea when to put 2kpi or kpi in an equation. Does is change for sin, cos, tan etc. Thanks so much.
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The 2kpi and kpi is the frequency in which you get the same answer.
For example, when does sin theta = 0, when theta = 0, pi, 2pi, 3pi, 4pi, ..., npi, so this would meet the criteria of using kpi, since all these give a 0.
What about sin theta = 1, this happens at (1/2)pi, (1/2)pi + 2pi, (1/2)pi + 4pi, which takes the pattern (1/2)pi + 2kpi. k = 0: (1/2)pi; k = 1: (1/2)pi + 2pi; k = 2: (1/2)pi + 4pi.
If you add pi to 1/2pi, the sin is –1, which gives 3/2pi + 2kpi.
This occurs with all the trig functions: cos & tan.
The way to attack the problem is to look for the pattern, by writing down where the occurrence happens, tan theta = 1, 1/4pi (1st quadrant) and 5/4pi (3rd quadrant) and see if it fits the k or 2k pattern, and in this case the k pattern.
Another tip: Start at the origin with +x, +y values which gives Quadrant 1 (call this 'A'), and move counter clockwise numbering the quadrants.
-x, +y values is Quadrant 2 (call this 'S')
-x, -y values is Quadrant 3 (call this 'T')
x, -y values is Quadrant 4 (call this 'C')
So it would like SA (line 1) and TC line 2.
The importance of this:
"A": All are positive: sin, cos, & tan
"S": Only sin is positive
"T": Only tan is positive
"C": Only cos is positive
How to remember, start in Quadrant 1, moving counterclockwise: All Students Take Calculus
For example, when does sin theta = 0, when theta = 0, pi, 2pi, 3pi, 4pi, ..., npi, so this would meet the criteria of using kpi, since all these give a 0.
What about sin theta = 1, this happens at (1/2)pi, (1/2)pi + 2pi, (1/2)pi + 4pi, which takes the pattern (1/2)pi + 2kpi. k = 0: (1/2)pi; k = 1: (1/2)pi + 2pi; k = 2: (1/2)pi + 4pi.
If you add pi to 1/2pi, the sin is –1, which gives 3/2pi + 2kpi.
This occurs with all the trig functions: cos & tan.
The way to attack the problem is to look for the pattern, by writing down where the occurrence happens, tan theta = 1, 1/4pi (1st quadrant) and 5/4pi (3rd quadrant) and see if it fits the k or 2k pattern, and in this case the k pattern.
Another tip: Start at the origin with +x, +y values which gives Quadrant 1 (call this 'A'), and move counter clockwise numbering the quadrants.
-x, +y values is Quadrant 2 (call this 'S')
-x, -y values is Quadrant 3 (call this 'T')
x, -y values is Quadrant 4 (call this 'C')
So it would like SA (line 1) and TC line 2.
The importance of this:
"A": All are positive: sin, cos, & tan
"S": Only sin is positive
"T": Only tan is positive
"C": Only cos is positive
How to remember, start in Quadrant 1, moving counterclockwise: All Students Take Calculus
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sin and cos have a period of 2π, so when you find solutions for unit circle,
just add 2kπ
tan has period of π, so when you find solution, just add kπ
just add 2kπ
tan has period of π, so when you find solution, just add kπ