Verify That the Equation Is an Identity $P _ { 1 } = 4 \sin ( 400 \pi t )$

Verify that the equation is an identity.
-Two sound waves, producing the pressures $P _ { 1 } = 4 \sin ( 400 \pi t )$ and $P _ { 2 } = 3 \cos ( 400 \pi t )$ , combine on a person's ear drum to produce the pressure $\mathrm { P } = \mathrm { P } _ { 1 } + \mathrm { P } _ { 2 }$ . Graph $\mathrm { P }$ in $[ - 0.01,0.01,0.001 ]$ by $[ - 20,20,2 ]$ and use the graph to estimate values for $\mathrm { a }$ and $\mathrm { k }$ so that $\mathrm { P } = \mathrm { a } \sin ( 400 \pi \mathrm { t } + \mathrm { k } )$ . Round $\mathrm { k }$ to the nearest ten-thousandth, if necessary.

A) $\mathrm { a } = 2.2 ; \mathrm { k } = 0.9273$
B) $\mathrm { a } = 5 ; \mathrm { k } = 0.6435$
C) $a = 5 ; k = 808.6467$
D) $\mathrm { a } = 2.2 ; \mathrm { k } = 808.6467$

Correct Answer:

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