![\rm \vec u=\ \textless \ 7,2\ \textgreater \ \qquad\qquad\qquad v=\ \textless \ 0,-4\ \textgreater \](https://tex.z-dn.net/?f=%5Crm%20%5Cvec%20u%3D%5C%20%5Ctextless%20%5C%207%2C2%5C%20%5Ctextgreater%20%5C%20%5Cqquad%5Cqquad%5Cqquad%20v%3D%5C%20%5Ctextless%20%5C%200%2C-4%5C%20%5Ctextgreater%20%5C%20)
Recall that the cosine of the angle between the vectors is given by,
![\rm \cos\theta=\dfrac{\vec u\cdot\vec v}{|u||v|}](https://tex.z-dn.net/?f=%5Crm%20%5Ccos%5Ctheta%3D%5Cdfrac%7B%5Cvec%20u%5Ccdot%5Cvec%20v%7D%7B%7Cu%7C%7Cv%7C%7D)
So we have a bunch of things we need to do.
Find the dot product of u and v,
![\rm \vec u\cdot \vec v=\ \textless \ 7,2\ \textgreater \ \cdot\ \textless \ 0,-4\ \textgreater \ =7(0)+2(-4)=-8](https://tex.z-dn.net/?f=%5Crm%20%5Cvec%20u%5Ccdot%20%5Cvec%20v%3D%5C%20%5Ctextless%20%5C%207%2C2%5C%20%5Ctextgreater%20%5C%20%5Ccdot%5C%20%5Ctextless%20%5C%200%2C-4%5C%20%5Ctextgreater%20%5C%20%3D7%280%29%2B2%28-4%29%3D-8)
That gives us our numerator,
![\rm \cos\theta=\dfrac{-8}{|u||v|}](https://tex.z-dn.net/?f=%5Crm%20%5Ccos%5Ctheta%3D%5Cdfrac%7B-8%7D%7B%7Cu%7C%7Cv%7C%7D)
Find the magnitude of each vector,
![\rm |u|=\sqrt{7^2+2^2}=\sqrt{53}\qquad\qquad |v|=\sqrt{0^2+(-4)^2}=4](https://tex.z-dn.net/?f=%5Crm%20%7Cu%7C%3D%5Csqrt%7B7%5E2%2B2%5E2%7D%3D%5Csqrt%7B53%7D%5Cqquad%5Cqquad%20%7Cv%7C%3D%5Csqrt%7B0%5E2%2B%28-4%29%5E2%7D%3D4)
Ok that gives us our denominator,
![\rm \cos\theta=\dfrac{-8}{4\sqrt{53}}](https://tex.z-dn.net/?f=%5Crm%20%5Ccos%5Ctheta%3D%5Cdfrac%7B-8%7D%7B4%5Csqrt%7B53%7D%7D)
To find your angle theta, apply inverse cosine,
![\rm \cos^{-1}\left(\dfrac{-8}{4\sqrt{53}}\right)=\theta](https://tex.z-dn.net/?f=%5Crm%20%5Ccos%5E%7B-1%7D%5Cleft%28%5Cdfrac%7B-8%7D%7B4%5Csqrt%7B53%7D%7D%5Cright%29%3D%5Ctheta)
Let your calculator do the rest.
Hope that helps!