Use the Fundamental Identities to Find the Value of the Trigonometric

Multiple Choice

Use the fundamental identities to find the value of the trigonometric function.
-An airplane flying faster than the speed of sound creates sound waves that form a cone. If $\theta$ is the vertex angle of the cone and $\mathrm { m }$ is the Mach number for the speed of the plane, then $\sin \frac { \theta } { 2 } = \frac { 1 } { \mathrm {~m} }$ $( \mathrm { m } > 1 )$ . Find $\theta$ to the nearest degree if $\mathrm { m } = 2.9$ .

A) $45 ^ { \circ }$
B) $43 ^ { \circ }$
C) $38 ^ { \circ }$
D) $40 ^ { \circ }$