SOLUTION: For what values of θ is the tangent 0? For what values of θ is the tangent undefined? Please explain.

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Question 1079623: For what values of θ is the tangent 0? For what values of θ is the tangent undefined? Please explain.
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
θ is the greek letter theta

tan(theta) = sin(theta)/cos(theta)

If tan(theta) = 0, then sin(theta)/cos(theta) = 0 meaning that sin(theta) has to be zero. The denominator can never be zero or else things are undefined.

If sin(theta) = 0, then theta = 0 or theta = pi radians because this is where the y coordinate of the point on the unit circle is 0.

So if theta is restricted to the interval [0, 2pi), then tan(theta)=0 when theta = 0 or when theta = pi

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Tangent is undefined when the denominator cosine is zero.

cos(theta) = 0 only when theta = pi/2 or theta = 3pi/2. Notice this is where the x coordinate is now zero. Again refer to the unit circle.

So, tan(theta) is undefined when theta = pi/2 or theta = 3pi/2 assuming our restricted interval is [0,2pi).

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The tangent function is [ vertical ] / [ horizontal ]
The vertical displacement is zero in 2 cases:
+theta+=+0+
+theta+=+pi+
-----------------
+tan%280%29+=+0%2F1+
+tan%28+pi+%29+=+0%2F%28-1%29+
==================
The horizontal displacement is zero in 2 cases,
+theta+=+pi%2F2+
+theta+=+3pi%2F2+
This makes the tangent function undefined
+tan%28+pi%2F2+%29+ = infinity
+tan%28+3pi%2F2%29+ = infinity
--------------------------
Hope this helps