functions of y= -x x>0

Amy

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Jun 24, 2004, 1:08:10 PM6/24/04

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I need to find all the trig. functions for an angle in statndard
position having its terminal side defined by the equation y = - x.

I can not get started, any suggestions would be great.

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Lynn Kurtz

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Jun 25, 2004, 3:33:10 AM6/25/04

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On Thu, 24 Jun 2004 17:08:10 GMT, Amy <tiffanyf...@hotmail.com>
wrote:

>I need to find all the trig. functions for an angle in statndard
>position having its terminal side defined by the equation y = - x.
>
>I can not get started, any suggestions would be great.

Take a piece of paper, put an xy coordinate system on it, and draw the
line y = -x. Draw an angle with initial side the positive x axis and
terminal side the line y = -x. You can do this for each of two
quadrants for your terminal side. The figure out the relevant angles
and determine their trig functions with appropriate signs.

--Lynn

gilgames

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Jun 25, 2004, 3:34:30 AM6/25/04

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Here is an approximation for 3 decimals. Change the function and the
limits and click submit. Click program tab to see the program.

http://lzkiss.netfirms.com/cgi-bin/igperl/igp.pl?dir=functions&name=trigtest

Jerschil

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Jul 6, 2004, 11:59:43 PM7/6/04

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y = -x st. x > 0 places the terminal side in the fourth quadrant at -45 degrees
or 315 degrees. As a result, you may find the 6 trig values for the given
angle.

Darrell

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Aug 23, 2005, 6:17:24 PM8/23/05

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"Amy" <tiffanyf...@hotmail.com> wrote in message
news:rk2md05pcgab58qe4...@4ax.com...

> I need to find all the trig. functions for an angle in statndard
> position having its terminal side defined by the equation y = - x.

In addition to what Lynn advised: When 'converting' equations of
nonvertical lines into angles in standard position, you may find useful (at
times a least) to 'figure out the relevant angle' with the relationship:

tan(angle) = slope

Determine the slope with usual means and plug it into the formula, giving in
this case:

tan(angle) = -1

...and solve for the 'angle'. Geometrically, using right triangle ratios,
you have a right triangle with opposite and adjacent sides both 1. Remember
"-1" has an understood denominator of 1. Don't worry too much about
signs(+/-) at this point; just worry about the numbers, so at this point you
have a right triangle with both legs of 1. Even if you don't already
recognize what kind of special triangle this is, or in cases where it's NOT
a special triangle, you can always use Pythagoras to solve for the remaining
side, thus allowing you to determine all six trig ratios of the angle.

For the signs(+/-) you said x>0, meaning the terminal side of the angle lies
in Q4 such that 3pi/2<angle<2pi, so keep that in mind when determining the
signs(+/-) of the other trig functions, too.

Q1 all positive
Q2 sine and its reciprocal (cosecant) are positive
Q3 tangent and its reciprocal (cotangent) are positive
Q4 cosine and its reciprocal (secant) are positive

--
Darrell