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### Evaluating a Trigonometric Expression

```
Date: 07/31/99 at 10:50:26
From: Alireza Rabi
Subject: Evaluation of a Trigonometric Expression

Can you help me evaluate tan(arcsin(3/5))? I think first we have to
find the angle for which the sine is 3/5, and then take the tangent of
it. We have to solve this problem with the sin^2(x)+cos^2(x) = 1.
```

```
Date: 07/31/99 at 20:53:16
From: Doctor Peterson
Subject: Re: Evaluation of a Trigonometric Expression

You have made a good start. Everything you have said is indeed part of
the solution.

Here is how I do this kind of problem, so that I do not have to
explicitly use sin^2(x)+cos^2(x) = 1 or do any algebra, but just sort

Draw a triangle (it does not have to have the right dimensions):

+
/|
/ |
/  |
/A  |
+----+

Now if we know the sine of A is 3/5, we can label the triangle:

+
/|
/ |
5/  |3
/A  |
+----+

Now you can use the Pythagorean Theorem (which is equivalent to the
identity you stated) to find the missing side, and from that you can
find the tangent.

Let me know if you need more help.

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Geometry
High School Triangles and Other Polygons
High School Trigonometry
Middle School Geometry
Middle School Triangles and Other Polygons

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