Question

Determine the ordered pair that represents the coordinates of the point where the terminal side of the angle measuring 245∘ intersects the unit circle, if the terminal side of an angle in standard position measuring 65∘ intersects the unit circle at (x,y)? Answer with an ordered pair in terms of x and y.

Answer 1

The point
$x = \sin \theta \: and \: y = cos \theta$
lies on the unit circle.


The reference angle for 245° is 65°.


Since 245° lies in the third quadrant,

cosine is negative and sine is negative

Therefore 245° intersect the unit circle at


$x = - \sin ( 65 \degree ) \: and \: y = - \cos(65 \degree)$
In terms of x and y, 245° intersects the unit circle at


$( - x,-y)$

Answer 2

Answer:

Step-by-step explanation:

For any circle in polar coordinates we write as

x= rcost and y = r sint

For unit circle r =1

Hence x = cost and y =sint

Here t = 245 lies in III quadrant,  Both sin and cos are negative

x = cos 245 =-0.4227

y =sin 245 =-0.9063

Hence ordered pair is

(-0.4227, -0.9063)