Write the given algebraic expression as a function of \( \theta \), where \( 0<\theta<\frac{\pi}{2} \), by making the given substitution. \( \sqrt{25-x^{2}} ; \) Substitute \( x=5 \sin \theta \) \( 5 \cos \theta \) \( 25 \sec \theta \) \( 25 \cos \theta \) \( 5 \sec \theta \)

Step 1: Start with the given expression \( \sqrt{25 - x^2} \). Step 2: Substitute \( x = 5 \sin \theta \) into the expression. This gives \( \sqrt{25 - (5 \sin \theta)^2} \). Step 3: Simplify the expression inside the square root: \( (5 \sin \theta)^2 = 25 \sin^2 \theta \). Step 4: Substitute this back into the expression: \( \sqrt{25 - 25 \sin^2 \theta} \). Step 5: Factor out 25 from the square root: \( \sqrt{25(1 - \sin^2 \theta)} \). Step 6: Use the Pythagorean identity \( 1 - \sin^2 \theta = \cos^2 \theta \): \( \sqrt{25 \cos^2 \theta} \). Step 7: Simplify the square root: \( 5 \cos \theta \).