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 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
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Re: Trig Help

Quote:
 Originally Posted by greg1313 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.
Yes but b is not part of x I thought?

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). $\displaystyle \csc^{\small-1}(5) = \sin^{\small-1}\left(\frac{\small1}{\small5}\right) = 0.201...$ Last edited by skipjack; August 26th, 2019 at 12:43 PM.

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