Question 1155732
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We can't find the exact values without knowing which quadrant we are in.<br>
Assume the angle is in quadrant I, so that all the function values are positive.  Then realize that any of the function values except the given value of sine might be negative.<br>
{{{sin^2(x)+cos^2(x)= 1}}}
{{{cos^2(x) = 1-sin^2(x)}}}
{{{cos(x) = sqrt(1-sin^2(x))}}}<br>
Plug in the given value of sin(x):<br>
{{{cos(x) = sqrt(1-(1/5))^2 = sqrt(1-1/25) = sqrt(24/25) = 2*sqrt(6)/5}}}<br>
Then use the values of sin(x) and cos(x) to find the values of the other functions.
{{{tan(x) = sin(x)/cos(x)}}}
{{{csc(x) = 1/sin(x)}}}
{{{sec(x) = 1/cos(x)}}}
{{{cot(x) = 1/tan(x)}}}<br>