Given that tan $2pi//9=0.8391$ , use equivalent trigonometric expressions to evaluate cot $5pi//18$ , to four decimal places?

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Answer 1 · 2018-04-24T19:20:17

$cot((5pi)/18)=0.8391$

$tan((2pi)/9)=0.8391$

$cot(pi/2 - Theta)=tan(Theta)$
$:.$
$cot((5pi)/18)=cot(pi/2 - (2pi)/9)=tan((2pi)/9)=0.8391$

Answer 2 · 2018-04-24T19:28:44

$0.8391$

$cot((5pi)/18)=cot((2pi)/9+pi/18)$

$color(green)(tan(a+b)=(tana+tanb)/(1-tana*tanb)$

$=1/(tan((2pi)/9+pi/18))=(1-tan((2pi)/9)*tan(pi/18))/(tan((2pi)/9)+tan(pi/18)$

$tan(pi/18)=0.17633$

$=(1-0.8391*0.17633)/(0.8391+0.17633)=0.8391$

Given that tan 2pi//9=0.83912pi//9=0.8391, use equivalent trigonometric expressions to evaluate cot 5pi//185pi//18, to four decimal places?