document.write( "Question 614417: \n" ); document.write( "

Algebra.Com's Answer #386544 by tam144(6) $\"\"$ $\"About$

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Problem: cos x = 2/3 ; tan x < 0 ; Find exact values of sin x.
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\n" ); document.write( "Suppose a calculator gives cos a1(deg.) = 2/3. On the trig unit circle, there are 2 arcs that have the same cos value (2/3). They are a1(deg.) and a2 = (360 - a1). The tan a2 is negative (< 0). The exact value of sin a2 is given by the trig identity:
\n" ); document.write( "sin^2 a2 = 1 - cos^2 a2 = 1 - 4/9 = 5/9.
\n" ); document.write( "There are 2 answers: sin a2 = 2.24/3 = 0.75 and sin a2 = -0.75, but only the negative value (-0.75) is the right answer.
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