Question

if sin theta is equal to root 3 by 2 find the value of all t ratio of theta​

Answer 1

sintheta =√3/2

then

costheta=1/2

tantheta=√3

cottheta=1/√3

cosectheta=2/√3

sectheta=2

Answer 2

$\sin(x) = \frac{ \sqrt{3} }{2} = \frac{p}{h} \\ so \\ \: p = \sqrt{3} \: and \: h = 2 \\ now \: using \: pythagoras \: theorem \\ {h}^{2} = {p}^{2} + {b}^{2} \\ {2 }^{2} = {( \sqrt{3}) }^{2} + {b}^{2} \\ {b}^{2} = 4 - 3 = 1 \\ b = 1 \\ now \\ \\ \cos(x) = \frac{b}{h} = \frac{1}{ 2} \\ \\ \tan( x ) = \frac{p}{b} = \frac{ \sqrt{3} }{1} \\ \\ \cot(x) = \frac{b}{p} = \frac{1}{ \sqrt{3} } \\ \\ \sec(x) = \frac{h}{b} = \frac{2}{1} \\ \\ \cosec(x) = \frac{h}{p} = \frac{2}{ \sqrt{3} }$

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