Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Proving trigonometric identities
Replies: 32   Last Post: Jan 27, 2009 1:59 AM

 Messages: [ Previous | Next ]
 Angus Rodgers Posts: 1,683 Registered: 7/16/07
Re: Proving trigonometric identities
Posted: Jan 24, 2009 4:37 AM

On Sat, 24 Jan 2009 00:56:58 -0800 (PST), Albert
<albert.xtheunknown0@gmail.com> wrote:

>Back to solving equations:
>Why does my booklet say 'none' to:
>Problem 3. Solving the following equations for 0 degrees <= x <= 360
>degrees.
>(a) ...
>(b) 3cosec x + 4 = 0;
>(c)...
>etc...
>
>3cosec x = -4
>cosec x = -4 / 3
>cosec x is quotient of the hypotenuse divided by the opposite. Our
>value here is negative and since the hypotenuse is always positive,
>the opposite side must be negative and hence the answer will be in one
>of the left quadrants (II or III).

Don't you mean a lower quadrant III or IV (assuming they are numbered
anticlockwise, starting from the positive quadrant, at the top right)?

>So then there are solutions to the
>equation, aren't there? and why/why not?

I'm a bit bleary-eyed, but it certainly does look to me as if (b) is
equivalent to sin x = -3/4, which has one solution for 180 degrees <
x < 270 degrees, one solution for 270 degrees < x < 360 degrees, and
no other solutions in the range indicated. (You'll need a calculator
to find the approximate values of x.)

--
Angus Rodgers

Date Subject Author
1/20/09 Albert
1/20/09 Angus Rodgers
1/20/09 Albert
1/20/09 Angus Rodgers
1/20/09 Albert
1/20/09 Angus Rodgers
1/20/09 Angus Rodgers
1/20/09 Guest
1/20/09 Angus Rodgers
1/20/09 Albert
1/20/09 Angus Rodgers
1/20/09 matt271829-news@yahoo.co.uk
1/21/09 Albert
1/21/09 matt271829-news@yahoo.co.uk
1/23/09 Albert
1/23/09 Angus Rodgers
1/23/09 Angus Rodgers
1/23/09 Passerby
1/23/09 Dave Dodson
1/24/09 Albert
1/24/09 Angus Rodgers
1/24/09 Albert
1/26/09 Albert
1/26/09 Driveby
1/26/09 Albert
1/26/09 A N Niel
1/27/09 Albert