Question

answer choices a. sin (pi/6)b. cos (pi/6)c. sin (pi/3)d. cos (pi/3)e. sin (2pi/3)f. cos (2pi/3)

Answer 1

The value of x - co-ordinate of point A is cos(2π/3)

Step - by - Step Explanation

Given that:

We know that if any unit circle which radius is r (r=1) and angle is θ then its coordinate will be:

x = rcos θ

y = r sinθ

In the figure given to us θ will be;

θ = π / 2 + π /6

$\theta=\frac{\pi}{2}+\frac{\pi}{6}$

Simplify

$\theta=\frac{3\pi+\pi}{6}$

$=\frac{4\pi}{6}$

We can reduce the fraction above by 2.

$=\frac{^2\cancel{4}\pi}{^3\cancel{6}}=\frac{2\pi}{3}$

But the x - coordinate is given by :

x= rcos θ

From the figure, it is a unit circle, so r = 1

We've calculated θ = 2π /3

Substitute the values into x = rcosθ

x = 1 . cos (2π /3)

Therefore, the value of x- coordinate is cos(2π/3)