Question

which of the following is true of the values of x and y in the diagram below? (diagram of unit circle with angle θ = π/4, point (x,y), and options y < x and y > x)

Explanation:

Step1: Find x using cosine

$x = r\cos\theta = 1\times\cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2} \approx 0.707$

Step2: Find y using sine

$y = r\sin\theta = 1\times\sin(\frac{\pi}{4}) = \frac{\sqrt{2}}{2} \approx 0.707$

Step3: Compare x and y

$x = y$

Answer:

(Note: Assuming the full options include "x = y"; if the given options are only y < x and y > x, but based on calculation x = y. However, if forced to choose from visible options, but standard unit circle at π/4 gives x=y.)

Wait, correction: The visible options are y < x and y > x, but the actual value is x=y. But maybe the diagram's angle is slightly more than π/4? No, π/4 gives equal x and y. So likely the full options have x=y. But based on the given diagram, x=y.

But since the user provided options as y < x and y > x (partial), but the correct relation is x=y. However, if the options are as shown, maybe a typo. But strictly from calculation: