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kuntzesses

Joined: Aug 13, 2008
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Having trouble solving some expressions

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The exercise tells me to use a right triangle to write each expression as an algebraic expression. It also says to assume x is positive and that the giveninverse trigonometric function is defined for the expression in x.

Here is one of the expressions. I would appreciate help on solving it so I can finish the exercise. As of right now I don't even know where to begin to draw the triangle or to solve the expression.

sin(tan^-1(x))

[Oct 21, 2008 12:35:53 PM]

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pskinner

Joined: Apr 2, 2005
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Re: Having trouble solving some expressions

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What is the sine of the angle whose tangent is x? The angle whose tangent is x has sides 1 and x so the hypotenuse is the square root of 1+x^2, so the sine is x over the square root of 1+x^2.
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Principal Skinner

[Oct 22, 2008 4:23:06 AM]

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kuntzesses

Joined: Aug 13, 2008
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Re: Having trouble solving some expressions

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Thank you for your help. I was hung up on the second side.

Was the 1 just assumed, and if so is this typical in this situation? Or was there a way you picked it out of the text?

Thanks again for all your help. I was able to complete my exercise with the information you provided me.

[Oct 22, 2008 9:38:48 PM]

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kuntzesses

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Re: Having trouble solving some expressions

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I think I understand where the 1 comes from now. It's because tan = opposite/adjacent

So in the problem I gave it could have also been written
sin(tan^-1(x/1))

Is this correct?
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[Edit 1 times, last edit by kuntzesses at Oct 23, 2008 1:24:23 PM]

[Oct 23, 2008 1:23:55 PM]

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pskinner

Joined: Apr 2, 2005
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Re: Having trouble solving some expressions

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I think I understand where the 1 comes from now. It's because tan = opposite/adjacent

So in the problem I gave it could have also been written
sin(tan^-1(x/1))

Is this correct?

Yes, the idea is that the trig functions can be thought of as ratio in a right triangle, so you need to write x as a ratio: x=x/1.
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Principal Skinner

[Oct 25, 2008 3:40:05 PM]

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