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February 15th, 2012, 02:12 PM   #1
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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.
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February 15th, 2012, 03:05 PM   #2
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Re: Trig Help

1) arctan(19/30)

2) Amplitude (peak to peak): 2, sin is � 1, 7 � 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.
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February 15th, 2012, 03:12 PM   #3
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Re: Trig Help

So the phase shift is:

To the left; (1/2)?
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February 15th, 2012, 03:20 PM   #4
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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.
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February 15th, 2012, 03:24 PM   #5
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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?
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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.
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February 15th, 2012, 03:47 PM   #7
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Re: Trig Help

y=A+BSinC(xD)
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?))
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February 15th, 2012, 09:43 PM   #8
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(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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