Question

5. Given a circle with a radius of 2 and a reference triangle of 30°. What are the sine andcosine of the angle?

Answer 1

We need to find sine and cosine for the angle formed by the triangle of reference of 30°, in the circle with a radius of 2.

To visualize better the exercise, we have the sketch below:

As the hypotenuse is 2, we can assume that the other two catheti are 1 (adjacent cathetus) and √3 (opposite cathetus).

And since the definition of the sine, we have that the value for it:

$sin(30)=\frac{\sqrt{3}}{2}$

And for the cosine:

$cos(30)=\frac{1}{2}=0.5$

Then we have that the correct answer are:

sin(30)=√3/2

cos(30)=1/2