Question

1. which equation would be used to solve for x? (see yellow hint below.) 25 in 13 in sin^{-1}x = \frac{13}{25} cos^{-1}x = \frac{13}{25} sin^{-1}x = \frac{25}{13} cos^{-1}x = \frac{25}{13}

Explanation:

Step1: Recall the definition of sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, for angle \(x\), the side opposite to \(x\) is \(13\) inches and the hypotenuse is \(25\) inches. So, \(\sin x=\frac{13}{25}\).

Step2: Use the inverse sine function

If \(\sin x = a\), then \(x=\sin^{-1}(a)\). From \(\sin x=\frac{13}{25}\), we can rewrite it as \(\sin^{-1}x=\frac{13}{25}\) (by the property of inverse functions, if \(y = \sin x\), then \(x=\sin^{-1}y\)).

Answer:

\(\sin^{-1}x=\frac{13}{25}\) (the first option)