Unit 33.7 Sinusoidal Function Context and Data ModelingCalculator required

Observation-wheel sensor trial

In an original synthetic trial, a seat sensor is 10 meters above ground at time 0 and rising. Its maximum height is 18 meters at 3 minutes, and its minimum height is 2 meters at 9 minutes. The motion repeats every 12 minutes.

Using $H(t)=10+8\sin(\pi t/6)$ , what height is predicted at $t=4.7$ minutes, to the nearest tenth?

12.0 m
15.0 m
17.9 m
20.0 m

Answer and derivation

Correct answer: B

$H(4.7)\approx15.034$ , so the predicted height is 15.0 meters.

Substitute 4.7 into the time variable.
In radian mode, evaluate $10+8\sin(4.7\pi/6)$ .
Round once at the end to 15.0 meters.

Why the other options fail

A: This can result from degree mode.
B: Correct radian evaluation and rounding.
C: This treats 4.7 as too close to the three-minute maximum.
D: This adds amplitude and maximum rather than evaluating the model.

Common misconception: Trigonometric model inputs inherit the angle unit encoded in the coefficient.

China/AP bridge: China-course bridge: substitution is familiar; AP newly expects students to support a contextual prediction with mode, units, and precision; unlike copying a display, state meters and rounding; a common pitfall is degree mode or missing parentheses.

Observation-wheel sensor trial

Using H(t)=10+8sin⁡(πt/6)H(t)=10+8\sin(\pi t/6)H(t)=10+8sin(πt/6), what height is predicted at t=4.7t=4.7t=4.7 minutes, to the nearest tenth?

Correct answer: B

Why the other options fail

Using $H(t)=10+8\sin(\pi t/6)$ , what height is predicted at $t=4.7$ minutes, to the nearest tenth?