Question

I wanted to get a quick check on my study answers

Answer 1

If an angle θ in standard position intersects the unit circle in a given position (x,y), we can say that:

`\tan \theta=(y)/(x)`

So, in 1, we got this intercection in

`(-(12)/(37),(35)/(37))`

So,

`\tan \theta=((35)/(37))/(-(12)/(37))=-(35)/(37)(37)/(12)=-(35)/(12)\approx-2.92`

In 2, to find the cossine, we first need the hypotenuse. The hypotenuse, in this case, is the radius fo the circle, which is one because it is a unit circle. So, we must do the adjacent leg divided by the hypotenus. The adjacent leg is equivalent to the x of the coordinate, so, for:

`((40)/(41),(9)/(41))`

We got:

`\cos \theta=((40)/(41))/(1)=(40)/(41)\approx0.976`

In 3, we just have to calculate

`\tan (-(11\pi)/(34))=-\tan ((11\pi)/(34))=-1.615`