What is the value of the x-coordinate of point A? (a) sin(pi/5)
(b) cos (pi/5)
(c) sin (6pi/5)
(d) cos (6pi/5)
(e) sin (9pi/5)

D.) cos(6π/5)

Step-by-step explanation:

In a unit circle, cosine is defined as x-coordinate and sine is defined as y-coordinate.

This is because cosine is defined as x/r but since it’s a unit circle, r = 1 therefore, cosine = x,

Sine is defined as y/r but it’s a unit circle so sine = y.

Therefore, we ignore choices with sine.

Next, since this π/5 angle is in the third quadrant. π/5 is supposed to be in the first quadrant so to convert from first quadrant angle or reference angle to the third quadrant angle or opposite side, add the reference angle or π/5 by π.

Therefore, π/5 + π = π/5 + 5π/5

= 6π/5

Since we want to find x-coordinate which is cosine, therefore.

The answer is cos(6π/5)

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