Question 802602
I challenge the previous answer's correctness, which states as follows:

Given that theta = 17pi/6, find the exact values of the sin, cos and tan of theta.
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What you need to know is the reference angle of given angle theta=17π/6, and which quadrant it is in.
17π/6 is like rotating counter-clockwise around the unit circle 16π plus an additional π/6, which places the reference angle of π/6 in quadrant I.
sin(17π/6)=sin(π/6)=1/2
cos(17π/6)=cos(π/6)=√3/2
tan(17π/6)=tan(π/6)=sin/cos=1/√3=√3/3

The above solution is incorrect.

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Correct Answer:

If theta = 17π/6, then when finding the quadrant, 

The mistake above is in finding the correct quadrant of the unit circle.

Rotating 17π/6 is NOT "like rotating counter-clockwise around the unit circle 16π plus an additional π/6."

It is rotating 2π then an additional 5π/6, or rotating 3π minus π/6, which would place it in quadrant II.

Thus, 


{{{sin((17pi)/6)=sin(2pi+5pi/6)=1/2}}}
{{{cos((17pi)/6)=cos(3pi-pi/6)=-cos(pi/6)=-sqrt(3)/2}}}
{{{tan((17pi)/6)=tan(3pi-pi/6)=tan(-pi/6)=-1/sqrt(3)=-sqrt(3)/3}}}

QED