Questions: Solve this sine function. sin^(-1)(sin 60°)=?

Solution Steps

To solve the given sine function, we need to understand the properties of the inverse sine function (arcsine). The arcsine function, \(\sin^{-1}(x)\), returns the angle whose sine is \(x\). Since \(60^\circ\) is within the range of the sine function, we can directly use the value.

• Convert \(60^\circ\) to radians because the sine function in Python uses radians.
• Use the sine function to find the sine of \(60^\circ\).
• Use the arcsine function to find the angle whose sine is the result from the previous step.

To work with the sine function, we first convert \(60^\circ\) to radians: \[ \text{angle\_in\_radians} = \frac{\pi}{3} \approx 1.0472 \]

Next, we calculate the sine of \(60^\circ\): \[ \sin(60^\circ) = \sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2} \approx 0.8660 \]

Now, we find the angle whose sine is \(0.8660\): \[ \sin^{-1}(0.8660) \approx 59.9999^\circ \]

Final Answer