document.write( "Question 1079623: For what values of θ is the tangent 0? For what values of θ is the tangent undefined? Please explain. \n" ); document.write( "
Algebra.Com's Answer #693845 by jim_thompson5910(35256)\"\" \"About 
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θ is the greek letter theta\r
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\n" ); document.write( "\n" ); document.write( "tan(theta) = sin(theta)/cos(theta)\r
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\n" ); document.write( "\n" ); document.write( "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.\r
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\n" ); document.write( "\n" ); document.write( "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.\r
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\n" ); document.write( "\n" ); document.write( "So if theta is restricted to the interval [0, 2pi), then tan(theta)=0 when theta = 0 or when theta = pi\r
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\n" ); document.write( "\n" ); document.write( "Tangent is undefined when the denominator cosine is zero. \r
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\n" ); document.write( "\n" ); document.write( "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.\r
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\n" ); document.write( "\n" ); document.write( "So, tan(theta) is undefined when theta = pi/2 or theta = 3pi/2 assuming our restricted interval is [0,2pi). \n" ); document.write( "
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