Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-The grade resistance $\mathrm { F }$ of a car traveling up or down a hill is modeled by the equation $\mathrm { F } = \mathrm { W } \sin \theta$ , where $W$ is the weight of the car and $\theta$ is the angle of the hill's grade $( \theta > 0$ for uphill travel, $\theta < 0$ for downhill travel) . What is the grade resistance (to the nearest pound) of a $3000 - \mathrm { lb }$ car traveling uphill on a $3 ^ { \circ }$ grade $\left( \theta = 3 ^ { \circ } \right)$ ?

Question

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-The grade resistance $\mathrm { F }$ of a car traveling up or down a hill is modeled by the equation $\mathrm { F } = \mathrm { W } \sin \theta$, where $W$ is the weight of the car and $\theta$ is the angle of the hill's grade $( \theta > 0$ for uphill travel, $\theta < 0$ for downhill travel). What is the grade resistance (to the nearest pound) of a $3000 - \mathrm { lb }$ car traveling uphill on a $3 ^ { \circ }$ grade $\left( \theta = 3 ^ { \circ } \right)$ ?
A) $- 3003 \mathrm { lb }$
B) $- 157 \mathrm { lb }$
C) $157 \mathrm { lb }$
D) $3003 \mathrm { lb }$

Quizplus · Accepted Answer

To find the grade resistance, substitute $W = 3000$ lb and $\theta = 3^\circ$ into the equation $F = W \sin \theta$. First, convert $3^\circ$ to radians because the sine function in calculators often uses radians. $3^\circ = \frac{3\pi}{180}$ radians. Then, calculate $F = 3000 \sin(\frac{3\pi}{180})$. Using a calculator, this gives $F \approx 157$ lb, rounded to the nearest pound.

Use a Calculator to Find the Function Value F\mathrm { F }F

Use a Calculator to Find the Function Value $\mathrm { F }$