Trig Function Applications

What is the maximum value of the following trig function?
 $y=8\cos\left(\frac{3\pi t-3\pi}{5}\right)+2.5$  

• 8

• 2.5

•  $\frac{3\pi}{5}$  

• 10.5

Answer explanation

Max value of cos is 1... 8*1+2.5 = 10.5

What is the "middle" value of the following trig function?
 $y=8\cos\left(\frac{3\pi t-3\pi}{5}\right)+2.5$  

• 8

• 2.5

•  $\frac{3\pi}{5}$  

• 10.5

Answer explanation

Middle value of cos is 0... 8*0+2.5 = 2.5

What is the period of the following trig function? $y=24\sin\left(\frac{\pi x-3\pi}{6}\right)+54$  

• 12

•  $\frac{\pi}{6}$  

•  $12\pi$  

• 24

Answer explanation

The horizontal stretch factor is  $\frac{\pi}{6}$  so use reciprocal... $2\pi\times\frac{6}{\pi}=12$  

What is the minimum value of the following trig function?
 $y=0.5\sin\left(\frac{\pi t-3\pi}{8}\right)+6$  

• -6

• -0.5

•  $\frac{3\pi}{8}$  

• 5.5

Answer explanation

Min value of sin is -1... 0.5*-1+6 = 5.5

What is the period of the following trig function? $y=3\cos\left(\frac{2\pi x-4\pi}{5}\right)$  

• 3

•  $\frac{2\pi}{5}$  

•  $\frac{5}{2\pi}$  

• 5

Answer explanation

The horizontal compression factor is  $\frac{2\pi}{5}$  so use reciprocal... $2\pi\times\frac{5}{2\pi}=5$  

A periodic scenario is found to have a max value of 10 after 2 minutes from the beginning of the observation. A min value of 2 was observed. Also, the max value occurs 6 minutes after the beginning of the observation. What cosine function would match this scenario?

• $y=4\cos\left(\frac{\pi x-2}{3}\right)+6$

• $y=4\cos\left(\frac{\pi x-2}{6}\right)+2$

• $y=8\cos\left(\frac{6\pi x-1}{2}\right)+10$

• $y=4\cos\left(\frac{2\pi x+2}{3}\right)+6$

Trigalicious?

• Kinda

• Most definitely

• Whatever