Question 1156023
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{{{cos(x) = 1/3}}}


{{{cos^2(x) = (1/3)^2}}} Square both sides


{{{cos^2(x) = 1/9}}}


{{{sin^2(x)+cos^2(x) = 1 }}} Pythagorean Trig Identity


{{{sin^2(x) = 1-cos^2(x) }}} Subtract cos^2(x) from both sides


{{{sin^2(x) = 1-1/9}}} Substitution


{{{sin^2(x) = 9/9-1/9}}}


{{{sin^2(x) = (9-1)/9}}}


{{{sin^2(x) = 8/9}}}


{{{sin(x) = sqrt(8/9)}}} Apply the square root to both sides. Sine is positive in quadrant 1


{{{sin(x) = sqrt(8)/sqrt(9)}}}


{{{sin(x) = sqrt(8)/3}}} <font color=red>This is one way to write the answer</font>


{{{sin(x) = sqrt(4*2)/3}}}


{{{sin(x) = sqrt(4)*sqrt(2)/3}}}


{{{sin(x) = 2*sqrt(2)/3}}} <font color=red>This is another equivalent way to write the answer</font>
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