# Trigonometry sin cos tan Question

#### 404

If Sin(theta) = 1/3 and cos(theta) < 0, find the value(s) for tan(theta)
How do I do this? Thanks.

#### mathwonk

Homework Helper
recall the emanings, with a picture, of these functions sin, cos, tan, using a unit circle. you may be able to just see it.

#### HallsofIvy

Homework Helper
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?

#### geometer

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.

#### 404

I got it now, Thanks guys :)

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