I Really Really Really Need Trig Help!!
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I Really Really Really Need Trig Help!!

[From: ] [author: ] [Date: 12-04-22] [Hit: ]
Thanks so much.-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,......
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

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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
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