Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
_____________________________________________
Associated Topics || Dr. Math Home || Search Dr. Math
_____________________________________________

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 
of "see" the answer.

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

Search the Dr. Math Library:


Find items containing (put spaces between keywords):
 
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

_____________________________________
Math Forum Home || Math Library || Quick Reference || Math Forum Search
_____________________________________

Ask Dr. MathTM
© 1994-2013 The Math Forum
http://mathforum.org/dr.math/