## Related questions with answers

During the course of treatment of an illness, the concentration of a drug (in micrograms per milliliter) in the bloodstream fluctuates during the dosing period of 8 hours according to the model

$C(t)=15.4-4.7 \sin \left(\frac{\pi}{4} t+\frac{\pi}{2}\right), \quad 0 \leq t \leq 8$

Use an identity to express the concentration $C(t)$ in terms of the cosine function. Note: This model does not apply to the first dose of the medication as there will be no medication in the bloodstream.

Solution

VerifiedUse sum identity for sine function.

$C(t)=15.4-4.7\left[\sin\left(\dfrac{\pi}{4}t\right)\cos\left(\dfrac{\pi}{2}\right)+\cos\left(\dfrac{\pi}{4}t\right)\sin\left(\dfrac{\pi}{2}\right)\right]$

Use $\cos\left(\dfrac{\pi}{2}\right)=0$ and $\sin\left(\dfrac{\pi}{2}\right)=1$.

$C(t)=15.4-4.7\cos\left(\dfrac{\pi}{4}t\right)$

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