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### Sin x^2, Sin^2 x, (Sinx)^2

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Date: 09/12/2001 at 09:51:32
From: Rob
Subject: Sin

What is the difference between sin x^2, sin^2 x, and (sinx)^2?
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Date: 09/12/2001 at 10:47:22
From: Doctor Ian
Subject: Re: Sin

Hi Rob,

Suppose x = pi/6, which means that sin x = 1/2.  Then

1. sin x^2 = sin ((pi/6)^2)

= sin (pi^2/36)

2. sin^2 x = (sin pi/4)^2

= (1/2)^2

= 1/4

3. (sin x)^2 = sin^2 x

It would seem pretty natural to think that

sin^2 x = sin(sin x)

but this isn't the convention that's been adopted.

Does this help?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
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Associated Topics:
High School Trigonometry

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