February 15th, 2012, 02:12 PM  #1 
Member Joined: Feb 2012 Posts: 78 Thanks: 0  Trig Help
I need to know how to do the following: 1.) Ethan is watching a satellite launch from an observation spot 6 miles away. Find the angle of elevation to the satellite, which is at a height of 3.8 miles. 2.) Find the Amp, period and phase shift of y=7+sin((3pi/4)x+(1/2)) This is what I have so far: Amp = 1 period = (8/3) phase shift = shift to the left (2/3pi) Is this right? 3.) Evaluate the following expression using a calculator if necessary. If the answer does not exist, write "does not exist". $\displaystyle \csc^{1} (5)$ Last edited by skipjack; August 26th, 2019 at 12:39 PM. 
February 15th, 2012, 03:05 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond  Re: Trig Help
1) arctan(19/30) 2) Amplitude (peak to peak): 2, sin is ï¿½ 1, 7 ï¿½ 1, 6 to 8 etc. Period: 8/3, 2$\pi$/(3$\pi$/4) = 8/3. Phase shift: 2/(3?) units to the left. Solve 3?x/4 = 1/2. 3) 1/sin(5), which exists since $\pi$ < 5 < 2$\pi$. Last edited by skipjack; August 26th, 2019 at 12:41 PM. 
February 15th, 2012, 03:12 PM  #3 
Member Joined: Feb 2012 Posts: 78 Thanks: 0  Re: Trig Help
So the phase shift is: To the left; (1/2)? 
February 15th, 2012, 03:20 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,963 Thanks: 1148 Math Focus: Elementary mathematics and beyond  Re: Trig Help
Phase shift: 2/(3$\pi$) units to the left. Solve 3$\pi$x/4 = 1/2. Sorry, I should have mentioned that this should be solved for x.
Last edited by skipjack; August 26th, 2019 at 12:42 PM. 
February 15th, 2012, 03:24 PM  #5 
Member Joined: Feb 2012 Posts: 78 Thanks: 0  Re: Trig Help
Here is what I got for the phase shift c/b= 1/2/(3pi)/4 = 1/2 x 4/(3pi) = 4/(6pi) = 2/(3pi) Therefore you phase shift to the left 2/(3pi) or do you take the reciprocal of that and shift to the right? 
February 15th, 2012, 03:25 PM  #6  
Member Joined: Feb 2012 Posts: 78 Thanks: 0  Re: Trig Help Quote:
Last edited by skipjack; August 26th, 2019 at 12:42 PM.  
February 15th, 2012, 03:47 PM  #7 
Senior Member Joined: Jan 2012 Posts: 131 Thanks: 0  Re: Trig Help
y=±A+BSinC(x±D) A=Vertical Shift +up,down B=Amplitude on Y axis. C=Horizontal Compression/Stretch. Period=2?/C D=Horizontal shift, + to the left,  to the right. y=7+sin((3pi/4)x+(1/2)) y=7+Sin(3?/4)(x+(1/2)/(3?/4)) y=7+Sin(3?/4)(x+(2/3?)) 
February 15th, 2012, 09:43 PM  #8 
Global Moderator Joined: Dec 2006 Posts: 20,966 Thanks: 2215 
(3). $\displaystyle \csc^{\small1}(5) = \sin^{\small1}\left(\frac{\small1}{\small5}\right) = 0.201...$
Last edited by skipjack; August 26th, 2019 at 12:43 PM. 

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