Question

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

Answer 1

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

Answer 2

Thee intersection point of the terminal side which measure the angle pi/6 radians  is (0.886, 0.5).

What is a circle?

It is a special kind of ellipse whose eccentricity is zero and foci are coincident with each other. It is a locus of a point drawn at an equidistant from the center.

The distance from the center to the circumference is called the radius of the circle.Given The terminal side of an angle measuring π/6 radians.

The coordinate point on the circle has to be find out It is known that, the formula for the coordinate is given by x = r cos∅   and y = r sin∅

Let the r be unity.

Then, x will be

$\rm x = cos \dfrac{\pi}{6} \\\\x = 0.866$

The variable y will be

$\rm y = sin \dfrac{\pi}{6} \\\\y = 0.5$

Thus, the intersection point is (0.886, 0.5).

Learn more about the circle here;

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