Questions: Find the exact value of the real number y if it exists. Do not use a calculator. y = cos^(-1)(1/2)

Solution Steps

To find the exact value of an inverse trigonometric function, recall the corresponding angle from the unit circle whose trigonometric function value matches the given number.

We need to find the value of \( y \) such that: \[ y = \cos^{-1}\left(\frac{1}{2}\right) \] This expression represents the angle whose cosine is \( \frac{1}{2} \).

From the unit circle, we know that: \[ \cos\left(\frac{\pi}{3}\right) = \frac{1}{2} \] Thus, the angle \( y \) that satisfies the equation is: \[ y = \frac{\pi}{3} \]

To express \( y \) in degrees, we can convert radians to degrees: \[ y_{\text{degrees}} = \frac{\pi}{3} \times \frac{180}{\pi} = 60 \]

Final Answer