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Author Topic: sec(1+2x)=sqrt(2)
mbarisas
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Icon 3 posted January 20, 2009 19:27      Profile for mbarisas     Send New Private Message       Edit/Delete Post   Reply With Quote 
Hi, I am completely stuck on this inverse trigonometry function. Is anyone willing to help??? ...I definitely need someone to break it down for me in step-by-step format.

I would be oh, so grateful.

the problem is:

sec(1+2x) = the square root of 2

Posts: 1 | From: california | Registered: Jan 2009  |  IP: Logged
The Famous Druid

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Icon 1 posted January 20, 2009 20:30      Profile for The Famous Druid     Send New Private Message       Edit/Delete Post   Reply With Quote 
Ok, I don't normally do other peoples homework for them, but today I'm in a "YES WE CAN" mood [Wink]

First, you need to know that...

sec(x) = 1/cos(x)
and
1/sqrt(2) = sqrt(1/2)

So your problem becomes...
1/cos(1+2x) = sqrt(2)

which easily becomes

cos(1+2x) = sqrt(1/2)

You should also recognise that cos(pi/4) = sqrt(1/2) (I'm assuming you're working in radians here)

So you're really solving for
(1+2x) = pi/4

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TheMoMan
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Icon 1 posted January 21, 2009 02:40      Profile for TheMoMan         Edit/Delete Post   Reply With Quote 
___________________ TFD __ Thanks for the reality check, I had forgotten about the COT, SEC,and CSC and had always just worked with the inverse of the three primary functions, cause my calc did not have said buttons. I must have looked at that expression for a minute and had still not figured out the problem until I read your solution.

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Posts: 5848 | From: Just South of the Huron National Forest, in the water shed of the Rifle River | Registered: Sep 2002  |  IP: Logged
spungo
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Icon 1 posted January 21, 2009 05:24      Profile for spungo     Send New Private Message       Edit/Delete Post   Reply With Quote 
quote:
Originally posted by The Famous Druid:
Ok, I don't normally do other peoples homework for them, but today I'm in a "YES WE CAN" mood [Wink]

First, you need to know that...

sec(x) = 1/cos(x)
and
1/sqrt(2) = sqrt(1/2)

So your problem becomes...
1/cos(1+2x) = sqrt(2)

which easily becomes

cos(1+2x) = sqrt(1/2)

You should also recognise that cos(pi/4) = sqrt(1/2) (I'm assuming you're working in radians here)

So you're really solving for
(1+2x) = pi/4

Small correction, old bean --

cos(2*n*pi +/- pi/4) = sqrt(1/2)

(where n is an integer). So,

1 + 2*x = 2*n*pi +/- pi/4

pedantic, I know, but tutors will pick up on that.

Furthermore, as sqrt(1/2) has two values (positive and negative), you could argue that there is another pair of solutions that satisfy the negative sqrt.

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Posts: 6529 | From: Noba Scoba | Registered: Jan 2002  |  IP: Logged


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