Question 1079623
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 <font color=red>theta = 0</font> or when <font color=red>theta = pi</font>


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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 <font color=red>theta = pi/2</font> or <font color=red>theta = 3pi/2</font> assuming our restricted interval is [0,2pi).