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### Basic Trig Identities

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Date: 09/15/97 at 03:14:55
From: Joyce
Subject: Basic Trig Identities

I am 15 and a junior in high school and currently taking a trig class.
It's only our 3rd week of school and I'm on question 1 and stuck

Solve each of the following for values of (it's a zero with a slash,
greek word theta) between ) 0 degrees and 90 degrees.

1. If sin (theta) = 3/4, find sec

I tried the reciprocal identity but that didn't work.

Thank you,

Joyce
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Date: 09/15/97 at 06:00:49
From: Doctor Mitteldorf
Subject: Re: Basic Trig Identities

Dear Joyce,

If you know one trig function of an angle, you can get them all.
To go from sin to cos, remember that the sum of the squares of the two
is 1. That's a result closely related to Pythagoras's famous theorem.
(The only trouble is that it sometimes leaves you wondering whether
to use plus the square root or minus; in the case you describe, with
the angle between 0 and 90, all the functions are positive.)

So we've gone from cos to sin or from sin to cos. To get tangent,
divide sin by cos. Sec is just 1/cos and Csc is just 1/sin (funny the
way that works isn't it - that the "co" is in opposite places for the
reciprocal functions.)

One more trick you need to know: how are you to go from tan back to
sin?  The trick here is to use "sec squared minus tan squared = 1".
That gets you from tan to sec, and then 1/sec is cos and 1-cos^2
is sin^2.

Hope this helps.

-Doctor Mitteldorf,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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Associated Topics:
High School Trigonometry

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