Question

d. the height of the wheel for a person riding a bike at a constant rate

1. if ( g(x) = sin(6x) + 3 ), determine ( g(15^circ) ).

a. ( g(15^circ) = 3.71 ) c. ( g(15^circ) = 4 )
b. ( g(15^circ) = 3 ) d. ( g(15^circ) = 3.87 )

Explanation:

Step1: Substitute \( x = 15^\circ \) into \( g(x) \)

We have the function \( g(x)=\sin(6x)+3 \). Substitute \( x = 15^\circ \) into the function, so we get \( g(15^\circ)=\sin(6\times15^\circ)+3 \).

Step2: Calculate the angle inside the sine function

First, calculate \( 6\times15^\circ = 90^\circ \). So now the function becomes \( g(15^\circ)=\sin(90^\circ)+3 \).

Step3: Evaluate the sine of \( 90^\circ \)

We know that \( \sin(90^\circ)=1 \) (from the unit - circle definition of the sine function, where at \( \theta = 90^\circ \), the \( y \) - coordinate of the point on the unit circle is 1).

Step4: Calculate the final value of \( g(15^\circ) \)

Substitute \( \sin(90^\circ)=1 \) into the function: \( g(15^\circ)=1 + 3=4 \).

Answer:

c. \( g(15^\circ)=4 \)