Use the Fundamental Identities to Find the Value of the Trigonometric

question 114

Multiple Choice

Use the fundamental identities to find the value of the trigonometric function.
-Two sound waves, producing the pressures $\mathrm { P } _ { 1 } = 8 \sin ( 460 \pi \mathrm { t } )$ and $\mathrm { P } _ { 2 } = 6 \cos ( 460 \pi \mathrm { t } )$ , 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 $a$ and $k$ so that $P = a \sin ( 460 \pi t + k )$ . Round $k$ to the nearest ten-thousandth, if necessary.

• A) \(\mathrm { a } = 3.2 ; \mathrm { k } = 929.9437\)
• B) \(a = 10 ; k = 929.9437\)
• C) \(a = 10 ; k = 0.6435\)
• D) \(a = 3.2 ; \mathrm { k } = 0.9273\)

---

Definitions:

$M

A shorthand notation for million dollars, used mainly in financial contexts to denote monetary values.

Interest Rate

The percentage charged on borrowed money, reflecting the cost of borrowing or the gain from saving.

Capital Projects

Large-scale investment projects that require significant amounts of capital, typically in infrastructure, buildings, or technology, aiming for long-term benefits.

Present Value

The current worth of a future sum of money or stream of cash flows given a specified rate of return, used in discounting to address the time value of money.