Solve the Problem $P _ { 1 } = 15 \sin ( 480 \pi t )$

Solve the problem.
-Two sound waves, producing the pressures $P _ { 1 } = 15 \sin ( 480 \pi t )$ and $P _ { 2 } = 8 \cos ( 480 \pi t )$ , combine on a person's ear drum to produce the pressure $P = P _ { 1 } + P _ { 2 }$ . Graph $P$ in $[ - 0.01,0.01,0.001 ]$ by $[ - 20,20,2 ]$ and use the graph to estimate values for $a$ and $k$ so that $P = a \sin ( 480 \pi t + k )$ . Round $k$ to the nearest ten-thousandth, if necessary.

A) $\mathrm { a } = 17 ; \mathrm { k } = 738.8376$
B) $\mathrm { a } = 4.1 ; \mathrm { k } = 1.0808$
C) $\mathrm { a } = 17 ; \mathrm { k } = 0.49$
D) $\mathrm { a } = 4.1 ; \mathrm { k } = 738.8376$

Correct Answer:

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