Answer:
(0.77, 0.64)
Step-by-step explanation:
To solve for the coordinates of point R which is on the circumference of the circle, we can construct a right triangle by drawing an auxiliary line from point R down to the x-axis that is perpendicular to the x-axis.
Then, we can use the sine and cosine ratios:
[tex]\rm \cos(\theta) = \dfrac{adjacent}{hypotenuse}[/tex]
[tex]\rm \sin(\theta) = \dfrac{opposite}{hypotenuse}[/tex]
to solve for the x- and y-coordinates, respectively, of point R.
This is possible because we know that the circle is a unit circle, which means that its radius is 1.
Constructing the cosine ratio gives us:
[tex]\cos(40\°) = \dfrac{x}{1}[/tex]
[tex]\implies x = \cos(40\°)[/tex]
And the sine ratio gives us:
[tex]\sin(40\°) = \dfrac{y}{1}[/tex]
[tex]\implies y = \sin(40\°)[/tex]
Evaluating these using a calculator set to degrees, we get:
[tex]x\approx 0.77[/tex]
[tex]y\approx0.64[/tex]
Finally, we can put these coordinates together in an ordered pair:
[tex]\huge\boxed{\dfrac{}{}(0.77, 0.64)\dfrac{}{}}[/tex]
