The angle y, whose cosine is -√2/2, is a reference angle for the cosine function. We can find the reference angle by taking the inverse cosine (arccos) of the given cosine value.
So, y = arccos(-√2/2)
Since the cosine function is negative in both the second and third quadrants, we know that the angle y must fall in one of these two quadrants.
The principal value of arccos(-√2/2) is π/4. However, since we're looking for an angle in the interval [0, π], the angle must be in the third quadrant.
To find the angle in the third quadrant, we subtract the principal value from π:
y = π - π/4
Simplifying, we have:
y = (4π - π)/4
y = 3π/4
Thus, the angle y, in radians, is y = 3π/4.
the angle y whose cosine is -sqrt2/2 and which is in the interval [0, pi] is y = x radians
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