Question

The terminal side of an angle measuring pi/6 radians intersects the unit circle at what point?

Answer 1

X = cos(pi/6) = √3/2

y = sin(pi/6) = 1/2

So at point (√3/2, 1/2)

Answer 2

ANSWER

It will intersect the unit circle at the point

$( \frac{ \sqrt{3} }{2} , \frac{1}{2} )$

EXPLANATION

The point
$(x = \cos( \theta) ,y=\sin(\theta))$
lies on the unit circle.

This explains the reason why
${x}^{2} + {y}^{2} = \cos ^{2} ( \theta) + \sin ^{2} ( \theta)$

The right hand side is the Pythagorean identity which simplifies to,

${x}^{2} + {y}^{2} = 1$

An angle whose terminal side measures
$\frac{ \pi}{6}$

will intersect the unit circle at

$(x = \cos( \frac{ \pi}{6} ) ,y=\sin( \frac{ \pi}{6} ))$

This simplifies to

$( \frac{ \sqrt{3} }{2} , \frac{1}{2} )$

See diagram