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/
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