Question 58 Answer and Explanation _ACT January 2009 Form 61F Math Section

58. The figure below shows the path of a certain projectile launched from the ground at an angle of θ. The horizontal range, r, of this projectile when launched from the ground at a speed of 20 meters per second is modeled by r = 40 sin (2θ) .

For this model, the angle measure θ that results in the greatest horizontal range, r, is 45° because:

F. 2 sin θ is greater than sin θ.

G. sin 90° is as large as sine can get.

H. sin 45° is as large as sine can get.

J. sin 45° is about 0.707.

K. sin 2θ is greater than sin θ.

Answer and Explanation

Your Answer is

Correct Answer is G

Explanation

When θ= 45°, sin (2θ) = sin (90°) = 1, and 1 is the maximum value of Sin(x), so choose G