Difference between revisions of "008A Sample Final A, Question 18"

Latest revision as of 23:04, 25 May 2015

Question: Compute $\cos(\arctan {\frac {5}{3}})$

Foundations:
1) Arctan can be thought of as referencing an angle in a triangle. What are the side lengths of the triangle?
Answer:
1) Since tangent is opposite/adjacent, the side lengths of the triangle are $3,5{\text{, and }}{\sqrt {34}}$

Solution:

Step 1:
$\arctan \left({\frac {5}{3}}\right)$ is the measure of an angle in the triangle with side lengths $3,5{\text{, and }}{\sqrt {34}}$ . The angle that corresponds to $\arctan \left({\frac {5}{3}}\right)$ is the one between the side of length 3 and the side of length ${\sqrt {34}}$

Step 2:
Now we just have to take $\cos$ of the angle referred to in step 1.

Final Answer:
$\cos \left(\arctan {\frac {5}{3}}\right)={\frac {5}{\sqrt {34}}}$

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-'''Question: ''' &nbsp; Compute <math>\cos(\arctan\frac{5}{3})</math>
+'''Question: ''' Compute <math>\cos(\arctan\frac{5}{3})</math>
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+!Foundations: &nbsp;
 |-
 |1) Arctan can be thought of as referencing an angle in a triangle. What are the side lengths of the triangle?
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-! Step 1:
+! Step 1: &nbsp;
 |-
 |<math>\arctan\left(\frac{5}{3}\right)</math> &nbsp; is the measure of an angle in the triangle with side lengths <math>3, 5\text{, and } \sqrt{34}</math>. The angle that corresponds to <math>\arctan\left(\frac{5}{3}\right)</math> is the one between the side of length 3 and the side of length &nbsp; <math> \sqrt{34}</math>
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-!Step 2:
+!Step 2: &nbsp;
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 |Now we just have to take <math>\cos</math>&nbsp; of the angle referred to in step 1.
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-! Final Answer:
+!Final Answer: &nbsp;
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 |<math>\cos\left(\arctan\frac{5}{3}\right) = \frac{5}{\sqrt{34}}</math>