Trigonometric Equation

Date: Fri, 11 Aug 1995 03:02:05 -0400
From: Anonymous
Subject: trigonometic equations

Question: I have this equation to solve in which I just don't know where
to start:

{x : 2sin(3x-1)+7 = 6.25, -Pi<x<Pi}

The < > mean greater than and equal to. "Pi" means 3.14...

I couldn't make those signs on my computer.

Thanks, Marc.

Date: Fri, 11 Aug 1995 10:20:57 -0400 (EDT)
Subject: Re: trigonometic equations

Hello there!

Well, to solve this, just take a little bit at a time:

2sin(3x - 1) + 7 = 6.25
2sin(3x - 1) = -.75
sin(3x - 1) = -.375

Now that it looks better, we can take the inverse sine of both sides:
3x - 1 = arcsin(-.375) = -.384 (assuming we're using radians and not degrees)
3x = .616
x = .205

Voila!

I hope this all made sense to you.

-K

Date: Sat, 12 Aug 1995
From: Anonymous
Subject: trigonometic equations

G'day,

I sent you a problem the other day and I have a few questions. You gave me
an answer assuming radians were the measurement.  What if degrees were the
measurement? Is it possible to have more than one answer and what is the
arcsin? I really appreciate this.

Thanks for your help!

Date: Sat, 12 Aug 1995 10:52:37 -0400 (EDT)
Subject: Re: trigonometic equations

Hey, no problem.

I'll address your second question first: Arcsin.  Arcsin is the inverse
function of Sin.  So for instance, since Sin(Pi/6) = 1/2, Arcsin(1/2) = Pi/6.
Arcsin(x) asks the question "what angle (in degrees or radians) has x as its
Sine?"  Since the output values of Sin have to be between -1 and 1, so do
the input values of Arcsin.

As for what would have happened if we had been using degrees instead
of radians, all that would have happened is that we would have gotten a
different value for Arcsin(-.375).  Remember that Arcsin spits out an angle
measurement; to get the degree version, we can take the radian version and
just convert to degrees: -.384 radians = -22.0 degrees.  (to convert from
radians to degrees, multiply by 180 and divide by Pi.  To go the other way,
multiply by Pi and divide by 180).

So there's your crash course.  Hope you enjoyed it!

-K