Difference between revisions of "005 Sample Final A, Question 15"

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|First, let <math>\theta=\tan^{-1}(x)</math>. Then, <math>\tan(\theta)=x</math>.
 
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| Now, we draw the right triangle corresponding to <math>\theta</math>. Two of the side lengths are 1 and x and the hypotenuse has length <math>\sqrt{x^2+1}</math>.
 
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| Since <math>\cos(\theta)=\frac{\mathrm{opposite}}{\mathrm{hypotenuse}}</math>, <math>\cos(\tan^{-1}(x))=\cos(\theta)=\frac{1}{\sqrt{x^2+1}}</math>.
 
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Revision as of 11:35, 20 May 2015

Question Find an equivalent algebraic expression for the following,

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cos(\tan^{-1}(x))}
Step 1:
First, let Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta=\tan^{-1}(x)} . Then, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tan(\theta)=x} .
Step 2:
Now, we draw the right triangle corresponding to Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \theta} . Two of the side lengths are 1 and x and the hypotenuse has length Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sqrt{x^2+1}} .
Step 3:
Since Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cos(\theta)=\frac{\mathrm{opposite}}{\mathrm{hypotenuse}}} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cos(\tan^{-1}(x))=\cos(\theta)=\frac{1}{\sqrt{x^2+1}}} .
Final Answer:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{\sqrt{x^2+1}}}
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