## Trigonometry (11th Edition) Clone

$45^{\circ}$
Step 1: We let $\textbf {u}=\langle 0,4 \rangle$ and $\textbf {v}=\langle -4,4 \rangle$ Step 2: The formula for finding the angle between a pair of vectors is $\cos\theta=\frac{\textbf {u}\cdot\textbf {v}}{|\textbf {u}||\textbf {v}|}$ Step 3: $\cos\theta=\frac{\langle 0,4 \rangle\cdot\langle -4,4 \rangle}{|\langle 0,4 \rangle||\langle -4,4 \rangle|}$ Step 4: $\cos\theta=\frac{0(-4)+4(4)}{\sqrt (0^{2}+4^{2})\cdot\sqrt ((-4)^{2}+4^{2})}$ Step 5: $\cos\theta=\frac{16}{\sqrt (0+16)\cdot\sqrt (16+16)}$ Step 6: $\cos\theta=\frac{16}{\sqrt (16)\cdot\sqrt (32)}$ Step 7: $\cos\theta=\frac{16}{4\times4\sqrt 2}$ Step 8: $\cos\theta=\frac{16}{16\sqrt 2}$ Step 9: $\cos\theta=\frac{1}{\sqrt 2}$ Step 10: $\theta=\cos^{-1}(\frac{1}{\sqrt 2})$ Step 11: Solving using the inverse cos function on the calculator, $\theta=\cos^{-1}(\frac{1}{\sqrt 2})=45^{\circ}$ The vectors are not orthogonal.