Did I Simplify This Trigonometric Expression Correctly?

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The discussion revolves around simplifying the trigonometric expression sqrt((tcost)^2 + (-tsint)^2). The initial attempt involved factoring out sin^2t + cos^2t and combining terms, leading to t*sqrt(2). However, participants pointed out that the correct approach is to factor inside the square root first. The final correct answer is |t|, not just t. This highlights the importance of proper factoring in trigonometric simplifications.
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Homework Statement


sqrt((tcost)^2+(-tsint)^2


Homework Equations





The Attempt at a Solution


pulled out the sin^2t+cos^2t
added the two t^2
took the sqrt of
t*sqrt(2)
 
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No, it's not correct. Factor the inside of the sqrt before you start 'pulling things out'.
 
so is the answer simply t
 
jimbo71 said:
so is the answer simply t

Almost right. |t| actually.
 

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