What are the six trig function values of $(5pi)/6$ ?

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Answer 1 · 2015-12-16T03:17:51

$(5pi)/6$ has a reference angle of $pi/6$ , so all its trig values will be related to the values for $pi/6$ .

Also notice that $(5pi)/6$ is located in the second quadrant, so...

$"SINE"$ will be positive.
$"COSINE"$ will be negative.

$sin(pi/6)=1/2$ , so $color(blue)(sin((5pi)/6)=1/2$ .

$cos(pi/6)=sqrt3/2$ , so $color(blue)(cos((5pi)/6)=-sqrt3/2$

$"TANGENT"$ is just $"SINE"$ divided by $"COSINE"$ :

$color(blue)(tan((5pi)/6))=(1/2)/(-sqrt3/2)=1/2(-2sqrt3)=-1/sqrt3color(blue)(=-sqrt3/3$

To figure out the other three, know that

$"SECANT"$ is the reciprocal of $"COSINE"$ ,
$"COSECANT"$ is the reciprocal of $"SINE"$ , and
$"COTANGENT"$ is the reciprocal of $"TANGENT"$ .

$color(blue)(sec((5pi)/6))=1/(-sqrt3/2)=-2/sqrt3color(blue)(=-(2sqrt3)/3$

$color(blue)(csc((5pi)/6))=1/(1/2)color(blue)(=2$

$color(blue)(cot((5pi)/6))=1/(sqrt3/3)=3/sqrt3color(blue)(=sqrt3$

What are the six trig function values of (5pi)/6(5pi)/6?