If an angle θ in standard position intersects the unit circle in a given position (x,y), we can say that:
[tex]\tan \theta=\frac{y}{x}[/tex]
So, in 1, we got this intercection in
[tex](-\frac{12}{37},\frac{35}{37})[/tex]
So,
[tex]\tan \theta=\frac{\frac{35}{37}}{-\frac{12}{37}}=-\frac{35}{37}\frac{37}{12}=-\frac{35}{12}\approx-2.92[/tex]
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:
[tex](\frac{40}{41},\frac{9}{41})[/tex]
We got:
[tex]\cos \theta=\frac{\frac{40}{41}}{1}=\frac{40}{41}\approx0.976[/tex]
In 3, we just have to calculate
[tex]\tan (-\frac{11\pi}{34})=-\tan (\frac{11\pi}{34})=-1.615[/tex]
