SOLUTION: Find tan(theta) if sin(theta) = -1 and 0 <= theta

SOLUTION: Find tan(theta) if sin(theta) = -1 and 0 <= theta < 2pi radions

Question 1159519: Find tan(theta) if sin(theta) = -1 and 0 <= theta < 2pi radions
Answer by greenestamps(13209) (Show Source): You can put this solution on YOUR website!

This truly is basic; a thorough understanding of this kind of question is necessary as you get deeper into the study of trigonometry.

You can use the unit circle or the graph of the sine function to find the answer; you should be able to do it either way.

With the unit circle, the sine of an angle is the y value. On the unit circle, what is the only angle at which the y value is -1?

With the graph of the sine function, on a full period 0 to 2pi radians, the graph starts at 0, rises to its maximum value of 1 at pi/2 radians, returns to 0 at pi, falls to its minimum value of -1 at 3pi/2 radians, and returns to 0 at 2pi. Again there is only one angle for which the value of the sine function is -1.

I again emphasize that if you are just starting your study of trigonometry you want to have a thorough understanding of the sine, cosine, and tangent functions in relation to the unit circle and to the graphs of those functions.

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