I have some arguments from trigonometry students and their teacher reasoning that for #24 (chapter 3) the answer would be 0. I know this text states on page 63 that Sin2theta is 1 but their reasoning being supported by the calculator is convincing. Would you be able to give more insight to this question?
Thank you.

Hi cmorales, thank you for your question. The textbook question asks "What is the maximum horizontal range of your gun?". The gun is able to shoot, since we're given data about how long a shot straight up takes to return to the gun. This data is useful to determine the initial velocity that's possible for the gun. With that initial velocity in mind, we can calculate the maximum possible range, and it will certainly be more than zero. The angle at which the range is maximum is $45^\circ$, and taking the sine of two times that gives "one", which is the greatest possible sine value of any angle. Keep in mind that we're maximizing horizontal range, not vertical height... I'm just guessing at where the misunderstanding might be...

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I have some arguments from trigonometry students and their teacher reasoning that for #24 (chapter 3) the answer would be 0. I know this text states on page 63 that Sin2theta is 1 but their reasoning being supported by the calculator is convincing. Would you be able to give more insight to this question?

Thank you.

Hi cmorales, thank you for your question. The textbook question asks "What is the maximum horizontal range of your gun?". The gun is able to shoot, since we're given data about how long a shot straight up takes to return to the gun. This data is useful to determine the initial velocity that's possible for the gun. With that initial velocity in mind, we can calculate the maximum possible range, and it will certainly be more than zero. The angle at which the range is maximum is $45^\circ$, and taking the sine of two times that gives "one", which is the greatest possible sine value of any angle. Keep in mind that we're maximizing horizontal range, not vertical height... I'm just guessing at where the misunderstanding might be...