document.write( "Question 697167: Please help me verify the identity of cot(θ-(pi)/(2))= -tanθ. I know that -tan0 is not a identity for the equation I just need help figuring out how to find it step by step
\n" ); document.write( "please and thank you so very much \n" ); document.write( "
Algebra.Com's Answer #429751 by lwsshak3(11628)\"\" \"About 
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Please help me verify the identity of cot(θ-(pi)/(2))= -tanθ
\n" ); document.write( "The best way I know how to verify this is with examples using a unit circle and reference angles.
\n" ); document.write( "I will use special angle 30º and degrees in place of radians for for ease of explanation.
\n" ); document.write( "First example:
\n" ); document.write( "Say, θ=30º in quadrant I where tan>0
\n" ); document.write( "The reference angle=30º
\n" ); document.write( "cot30º=√3
\n" ); document.write( "cot(θ-(pi)/(2)= cot(θ-90º)
\n" ); document.write( "This means you are moving θ, 90º clockwise which places the angle is quadrant IV, where cot<0
\n" ); document.write( "standard position of the angle=300º
\n" ); document.write( "The reference angle is =60º
\n" ); document.write( "cot(θ-(pi)/(2)= cot(θ-90º)=cot60º=-√3/3=-tan30º=-tanθ
\n" ); document.write( "..
\n" ); document.write( "Second example:
\n" ); document.write( "Say, θ=210º in quadrant III, where tan>0
\n" ); document.write( "The reference angle=30º
\n" ); document.write( "cot30º=√3
\n" ); document.write( "cot(θ-(pi)/(2)= cot(θ-90º)
\n" ); document.write( "This means you are moving θ, 90º clockwise which places the angle is quadrant II, where cot<0
\n" ); document.write( "standard position of the angle=120º
\n" ); document.write( "The reference angle is =60º
\n" ); document.write( "cot(θ-(pi)/(2)= cot(θ-90º)=cot60º=-√3/3=-tan210º=-tanθ
\n" ); document.write( "..
\n" ); document.write( "Third example:
\n" ); document.write( "Say, θ=330º in quadrant IV, where tan<0
\n" ); document.write( "The reference angle=30º
\n" ); document.write( "cotθ=cot30º=-√3
\n" ); document.write( "cot(θ-(pi)/(2)= cot(θ-90º)
\n" ); document.write( "This means you are moving θ, 90º clockwise which places the angle is quadrant II, where cot>0
\n" ); document.write( "standard position of the angle=240º
\n" ); document.write( "The reference angle is =60º
\n" ); document.write( "cot(θ-(pi)/(2)= cot(θ-90º)=cot60º=√3/3=-tan330º=-tanθ
\n" ); document.write( "..
\n" ); document.write( "Note:Only special angle of 30º is used in foregoing examples, but this will work with any angle.
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