Question

cos?¹(-1) If y = cos?¹ x, then cos y = x, 0 ? y ? ?. Therefore, to find y = cos?¹(-1), we must find the angle y whose cosine is -1. There are many possible angles with this cosine, but the range of y = cos?¹ x is restricted to [0, ?], and so y must be in this interval. The angle y whose cosine is -1 and which is in the interval [0, ?] is y = radians.

          cos?¹(-1)
If y = cos?¹ x, then cos y = x, 0 ? y ? ?. Therefore, to find y = cos?¹(-1), we must find the angle y whose cosine is -1.
There are many possible angles with this cosine, but the range of y = cos?¹ x is restricted to [0, ?], and so y must be in this interval.
The angle y whose cosine is -1 and which is in the interval [0, ?] is y = radians.

cos?¹(-1)
If y = cos?¹ x, then cos y = x, 0 ? y ? ?. Therefore, to find y = cos?¹(-1), we must find the angle y whose cosine is -1.
There are many possible angles with this cosine, but the range of y = cos?¹ x is restricted to [0, ?], and so y must be in this interval.
The angle y whose cosine is -1 and which is in the interval [0, ?] is y = radians.

Added by Julie C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zhumagali Shomanov

06/12/2023

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If y = cos⁻¹x, then cos y = x, 0 ≤ y ≤ π. Therefore, to find y = cos⁻¹(-1), we must find the angle y whose cosine is -1. There are many possible angles with this cosine, but the range of y = cos⁻¹x is restricted to [0, π], and so y must be in this interval. The angle y whose cosine is -1 and which is in the interval [0, π] is y = radians.