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how do you solve problems like: cos[arctan(-1)] ?? thanks everyone

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agvickers | Student, Grade 11 | Honors

Posted January 24, 2012 at 7:20 AM via web

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how do you solve problems like:

cos[arctan(-1)]

?? thanks everyone

Tagged with math, precalculus

2 Answers | Add Yours

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nathanshields | High School Teacher | (Level 1) Associate Educator

Posted January 24, 2012 at 7:29 AM (Answer #1)

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1. Tangent of what angle is -1?
2. What is cosine of this angle?

The tangent function is like the slope of a radius on the unit circle.  There are two that have a slope of -1: `135^o` and `315^o`

Let's just use the first one: `135^o` or `(3pi)/4` radians.

Take the cosine (visualize the adjacent and hypotenuse: `-sqrt(2)/2` and `1` ), and your answer is

`-sqrt(2)/2`

Notice that if you used the other angle, your answer would be

`sqrt(2)/2`

So you check what domain you want your answer to be in.

 

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agvickers | Student , Grade 11 | Honors

Posted January 25, 2012 at 11:48 AM (Answer #2)

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in the problem all i was given was this, and it wants me to use the properties of inverse functions......i dont really understand it yet...

 

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