Trigonometry sin cos tan Question

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Discussion Overview

The discussion revolves around finding the value(s) of tan(theta) given that Sin(theta) = 1/3 and cos(theta) < 0. The scope includes mathematical reasoning and conceptual clarification related to trigonometric functions.

Discussion Character

  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant asks how to find tan(theta) given the conditions on sin(theta) and cos(theta).
  • Another participant suggests using the unit circle to understand the meanings of sin, cos, and tan.
  • A different participant points out the identity sin²(theta) + cos²(theta) = 1 and suggests using the known value of sin(theta) to find cos(theta).
  • One participant proposes taking the arc sin of 1/3 to find the angle, noting that the angle must be in the second quadrant due to the conditions on cos(theta) and sin(theta).
  • A later reply indicates that the initial participant has understood the problem after the discussion.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a final method for calculating tan(theta), but there is a general agreement on the approach of using trigonometric identities and quadrant considerations.

Contextual Notes

The discussion does not resolve the specific calculations for tan(theta) and relies on assumptions about the quadrant in which theta lies based on the given conditions.

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If Sin(theta) = 1/3 and cos(theta) < 0, find the value(s) for tan(theta)

How do I do this? Thanks.
 
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recall the emanings, with a picture, of these functions sin, cos, tan, using a unit circle. you may be able to just see it.
 
Do you know that sin2(&theta;)+ cos2(&theta;)= 1? Since you know sin(&theta;)= 1/3, you can use that to find cos(&theta;). Now, how is tan(&theta;) defined?
 
404 said:
How do I do this? Thanks.

Take the arc sin of 1/3 - this will give you the angle, but it will be the principle angle (first quadrant). But, since Cos theta <0, you know it can't be in the first quadrant or fourth quadrant, so it must be in either the second or third quadrant. But, since sin theta is >0, it must be in the second quadrant. You should be able to get the correct angle from this info, and therefore the correct cosine and then - as was hinted before - remember the definition of tangent theta.
 
I got it now, Thanks guys :)
 

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