Answer:
[tex]\frac{\sqrt{2}}{2}[/tex]
Step-by-step explanation:
Start by determining the simpler angle [tex]2\pi-\theta[/tex] (or, the complement of the highlighted angle in red on your image). The cosine of that angle is
[tex]\cos (2\pi-\theta) = \frac{x}{1}=\frac{\frac{\sqrt{2}}{2}}{1}=\frac{\sqrt{2}}{2}[/tex]
Now, back to the actual red-circled angle. That one is going in the negative direction and ends up in the same position on the unit circle. Since cosine is an even function, its value is the same whether you evaluate at an angle theta, or its complement 2pi-theta. So, the final answer is: [tex]\frac{\sqrt{2}}{2}[/tex]
