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Q: Trigonometry ( No Answer,   1 Comment )
Subject: Trigonometry
Category: Reference, Education and News > Homework Help
Asked by: david0287-ga
List Price: $5.00
Posted: 29 Apr 2006 09:52 PDT
Expires: 29 Apr 2006 12:03 PDT
Question ID: 723943
I have read a few websites and a book on trigonometric identities and I know that:
cos x = sin 90 - x
cos^2 + sin^2 x = 1
sin x / cos x = tan x

I am not sure how to solve an equation whith z(sin x) and (cos y)
For example sovle the equation:
3(sin 20) = cos(2x)    [degrees]
(find x for 0 <= x <=180)

There is no answer at this time.

Subject: Re: Trigonometry
From: kottekoe-ga on 29 Apr 2006 11:50 PDT
In general, equations like this cannot be solved without invoking the
so-called inverse trigonometric functions. For example, to solve your
example for x:

z*sin(y) = cos(2x)

We could write:

2x = arccos(z*sin(y)), where arccos(a) is the inverse of the cosine function

Thus, we can formally solve it by saying:

x = arccos(z*sin(y))/2

Unfortunately, your example has no solution, since 3*sin(20) is bigger
than one and thus cannot equal cos(2x) for any value of x.

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