document.write( "Question 1077232: 7. If tan(x) = 2 and x ∈ [180◦ , 270◦ ]. Determine the value of
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Algebra.Com's Answer #691803 by math_helper(2461) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"tan%28x%29+=+2\"$ —> $\"+x=tan%5E-1%282%29+=+63.4349%5Eo+\"$ and since $\"+tan%28x%29+=+b%2Fa+\"$ : $\"+a=-1+\"$ , $\"b=-2\"$
\n" ); document.write( "But since we're in Q3, we need to add $\"180%5Eo\"$ to get it into standard form (where the angle is measured from the +x axis counterclockwise). \r
\n" ); document.write( "\n" ); document.write( "(iii) $\"+highlight%28x=243.4349%5Eo%29+\"$ in standard form.\r
\n" ); document.write( "\n" ); document.write( " $\"+h+=+sqrt%28a%5E2+%2B+b%5E2%29+=+sqrt%28%28-1%29%5E2%2B%28-2%29%5E2%29+=+sqrt%285%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "(i) $\"+cos%28x%29+=+a%2Fh+=+highlight%28-1%2Fsqrt%285%29%29+\"$ or approx. -0.447214
\n" ); document.write( "(ii) $\"+sin%28x%29+=+b%2Fh+=+highlight%28-2%2Fsqrt%285%29%29+\"$ or approx. -0.894427\r
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\n" ); document.write( "NOTE: Just be aware: often you will want to normalize things so you have a unit circle (i.e. r=1). I did not use a unit circle (h=sqrt(5)). To do that I would have had to divide a,b, and h by sqrt(5). However, since the problem only dealt with ratios of the sides, the lack of normalization didn't matter. \r
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